The Problems of Philosophy

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HOME UNIVERSITY LIBRARY
OF MODERN KNOWLEDGE
No. S6

Editors :

HERBERT
Prof.

FISHER, M.A., F.B.A.

GILBERT MURRAY,

Litt.D.,

LL.D., F.B.A.

Prof.
Prof.

J.

ARTHUR THOMSON,

W.LLIAM

T.

M.A.
M.A.

BREWSTER,

A

complete classified

Home

University

list

of the volumes tf

Library

already

will be found at the back of this book.

The

published

THE PROBLEMS
OF PHILOSOPHY
BY

BERTRAND RUSSELL
M.A., F.R.8.

LECTURER AND LATE FELLOW OF TRINITY COLLEGE
CAMBRIDGE

NEW YORK
HENRY HOLT AND COMPANY
LONDON
WILLIAMS AND N ORG ATE

PREFACE
In the following pages, I have confined
myself in the main to those problems of
philosophy in regard to which

I

thought

possible to say something positive and
constructive, since merely negative criticism
it

seemed out

For

this reason, theory
a
larger space than
knowledge occupies
metaphysics in the present volume, and some
of place.

of

topics

much

discussed

by philosophers are
at

all.
treated very briefly,
I have derived valuable assistance from
if

unpublished writings of Mr. G. E. Moore and
from the former, as reMr. J. M. Keynes
:

gards the relations of sense-data to physical
objects, and from the latter as regards probI have also profited
ability and induction.
greatly

by the

criticisms

Professor Gilbert Murray.

and suggestions

of

CONTENTS
CHAPTER
I

II

PAGE

APPEARANCE AND REALITY

.

.

9

THE EXISTENCE OF MATTER

.

.

26

III

THE NATURE OF MATTER

IV

IDEALISM

...

58

V KNOWLEDGE

BY

ACQUAINTANCE

KNOWLEDGE BY DESCRIPTION
VI

ON INDUCTION

Vn ON

OUR

IX

HOW

A PRIORI

AND

.

OF

KNOWLEDGE

IS

THE WORLD OF UNIVERSALS

ON INTUITIVE KNOWLEDGE
vii

.

72

93

GENERAL

POSSIBLE
.

X ON OUR KNOWLEDGE OF UNIVERSALS
XI

.

.....
.....

KNOWLEDGE

PRINCIPLES
VIII

42

.

109
127

.142
.

158

.174

CONTENTS

viii

PAOE

OHAPTEB

XII

TRUTH AND FALSEHOOD

Xin KNOWLEDGE,
OPINION

.

.

.

.....

ERROR,

186

AND PROBABLE
204

XIV THE LIMITS OF PHILOSOPHICAL KNOW-

LEDGE

220

XV THE VALUE OF PHILOSOPHY

.

.

BIBLIOGRAPHICAL NOTE

.

.251

INDEX

.

237

253

THE

PROBLEMS OF PHILOSOPHY
CHAPTER

I

APPEARANCE AND REALITY
any knowledge in the world which
is so certain that no reasonable man could
doubt it ? This question, which at first sight
Is there

might not seem difficult, is really one of the
most difficult that can be asked. When we
have realised the obstacles in the way of a
straightforward

and confident answer, we
on the study of philo-

shall be well launched



sophy for philosophy is merely the attempt
to answer such ultimate questions, not
carelessly and dogmatically, as we do in
ordinary

life

and even

critically, after

in the sciences,

exploring
9

all

but

that makes such

THE PROBLEMS OF PHILOSOPHY

10

queitions puzzling, and after realising all
the vagueness and confusion that underlie

our ordinary ideas.
In daily life, we assume as certain

many

things which, on a closer scrutiny, are found
to be so full of apparent contradictions that
only a great amount of thought enables us
to

know what

it is

we

that

really

may

believe.

In the search for certainty, it is natural to
begin with our present experiences, and in

no doubt, knowledge is to be
derived from them. But any statement as
to what it is that our immediate experiences

some

sense,

make us know
seems to

me

very likely to be wrong. It
that I am now sitting in a chair,
is

at a table of a certain shape, on which I see
sheets of paper with writing or print.
By

turning

my

head

I see

out of the window

I believe
buildings and clouds and the sun.
that the sun is about ninety-three million miles

from the earth that it is a hot globe many
times bigger than the earth that, owing to
;

;

the earth's rotation,

and

will

it

rises

every morning,
continue to do so for an indefinite

time in the future.

I

believe that,

if

any

APPEARANCE AND REALITY

11

other normal person comes into my room, he
will see the same chairs and tables and books

and papers as I see, and that the table which
I see is the same as the table which I feel
pressing against my arm. All this seems to
be so evident as to be hardly worth stating,

man who

except in answer to a

know

whether I

anything.

be reasonably doubted, and

much

Yet
all

of

careful discussion before

sure that

we have

stated

it

in a

doubts

all this
it

may

requires

we can be
form that

is

wholly true.

To make our

difficulties plain, let

centrate attention on the table.

us con-

To

the eye
oblong, brown and shiny, to the touch

it is

smooth and cool and hard when I
tap it, it gives out a wooden sound. Any one
else who sees and feels and hears the table
it

is

;

will agree

with this description, so that

it

might seem as if no difficulty would arise
but as soon as we try to be more precise our
;

troubles begin.
table

the

**

is

really

Although I believe that the
" of the same colour all
over,

the light look
other parts, and

parts that reflect

brighter than the

much
some

12

THE PROBLEMS OF PHILOSOPHY

parts look white because of reflected light.
I know that, if I move, the parts that rC'
fleet the light will be different, so that the

apparent distribution of colours on the table
change. It follows that if several people
are looking at the table at the same moment,
no two of them will see exactly the same
will

of colours,
because no two
from exactly the same point of
view, and any change in the point of view
makes some change in the way the light is

distribution

can see

it

reflected.

For most practical purposes these differences are unimportant, but to the painter
the painter has to
they are all-important
unlearn the habit of thinking that things
seem to have the colour which common sense
"
"
have, and to learn the
really
says they
:

habit of seeing things as they appear.

we have already the beginning

of

Here
one of

the distinctions that cause most trouble in
"
apphilosophy the distinction between
" and "
reality," between what
pearance



things seem to be and
painter wants to know

what they are. The
what tilings seem to

APPEARANCE AND REALITY
man and

be, the practical

want to know what
sopher's wish to

they are

know

the philosopher
; but the philo-

this is stronger

man's, and

13

than

more troubled by

the practical
knowledge as to the difficulties of answering
the question.
is

To return to the table. It is evident from
what we have found, that there is no colour
which pre-eminently appears to be the colour
of the table, or even of any one particular
part of the table it appears to be of different



colours from different points of view, and
there is no reason for regarding some of

these as

more

And we know

really its colour

that even from a given point

of view the colour will
artificial light,

to a

than others.

seem

different

by

or to a colour-blind man, or

man

wearing blue spectacles, while in
the dark there will be no colour at all, though
to touch and hearing the table will be unchanged. Thus colour is not something which
inherent in the table, but something depending upon the table and the spectator

is

and the way the

When,

in ordinary

light falls
life,

on the

we speak

table.

of the colour

U

THE PROBLEMS OF PHILOSOPHY

of the table,

we only mean the

sort of colour

seem to have to a normal
spectator from an ordinary point of view
under usual conditions of light. But the
other colours which appear under other
conditions have just as good a right to be
and therefore, to avoid
considered real
which

it

will

;

in itself,

we

are compelled to deny that,
the table has any one particular

favouritism,

colour.

The same thing applies to the texture.
With the naked eye one can see the grain,
but otherwise the table looks smooth and
If we looked at it through a microeven.
we
should see roughnesses and hills
scope,
and valleys, and all sorts of differences that
Which
are imperceptible to the naked eye.
of these

is

the "real" table?

rally tempted to say that
through the microscope is

We

are natu-

what we see
more real, but

Lliat in turn would be changed by a still
more powerful microscope.
If, then, we
cannot trust what we see with the naked
eye, why should we trust what we see

through a microscope

?

Thus,

again,

the

APPEARANCE AND REALITY

15

we

be-

confidence in our senses with which

gan deserts

The

us.

sha'pe of the table is

no

We

better.

all in the habit of judging as to the
" real "
shapes of things, and we do this so

are

unreflectingly that we come
actually see the real shapes.

as

we

all

have to learn

given thing looks

if

we

different

think

to

try to draw, a
in

shape from
If our table

every different point of view.
"
"
it will
is

almost
acute

all

points of view, as

and two

angles

if

from
had two

look,

rectangular,

really

we

But, in fact,

it

obtuse

angles.

If

opposite sides are parallel, they will look as
if they converged to a point away from the
spectator ; if they are of equal length, they
will look as if the nearer side were longer.
All these things are not

commonly

noticed

in looking at a table, because experience has
"
"
taught us to construct the real shape from

" real "
the apparent shape, and the
shape
But
is what interests us as practical men.
"
"
it
is
we
see
not
what
real
the
;
shape is

something inferred from what we

what we

see

is

see.

And

in

shape

constantly changing

16

THE PROBLEMS OF PHILOSOPHY
we move about the room

as

;

so that here

again the senses seem not to give us the truth
about the table itself, but only about the
appearance of the table.

when we

Similar difficulties arise

the sense of touch.

consider

It is true that the table

always gives us a sensation of hardness, and
we feel that it resists pressure. But the
sensation

we obtain depends upon how hard

we

press the table and also upon what part
of the body we press with
thus the various
;

sensations due to various pressures or various
parts of the body cannot be supposed to
reveal directly
table, but at

any definite property of the
most to be sig7is of some
which
property
perhaps causes all the senbut

sations,
of

them.

is

And

not actually apparent in any
the same applies still more

obviously to the sounds which can be elicited
by rapping the table.

Thus
if

it

there

is

becomes evident that the real table,
one, is not the same as what we

immediately experience by sight or touch or
hearing.

The

real table,

not immediately

known

if

there

to us at

all,

is

one,

is

but must

APPEARANCE AND REALITY
be an inference from what

Hence, two very

known.

at once arise
&t

;

namely,

(2) If so,

all ?

is

immediately

difficult

(1) Is there

what

17

questions
a real table

can

sort of object

it

be?
It will help us in considering these questions
to have a few simple terms of which the
is

meaning
the

name

of

definite

"

and

sense-data

Let us give
to the things that
in sensation
such

clear.

"

are immediately known
things as colours, sounds, smells, hardnesses,
shall give the
roughnesses, and so on.
:

We

name "

sensation

"

to

the

experience of
of these things.

being immediately aware
Thus, whenever we see a colour,

we have a

sensation of the colour, but the colour itself
is

a

colour

sense-datum, not a sensation. The
is that of which we are
immediately

aware, and the awareness itself is the sensation.
It

is

plain that

about the table,

we are to know anything
it must be by means of the

if

—brown colour,
—which we
smoothness,
sense-data

oblong

shape,

with
but for the reasons which have
been given, we cannot say that the table is the
etc.

the table

;

associate

THE PROBLEMS OF PHILOSOPHY

18

sense-data, or even that the sense-data are

properties of the table. Thus a
problem arises as to the relation of the sensedata to the real table, supposing there is
directly

such a thing.

The

real table,

"

if

it exists, we
Thus we have

will call a

to consider

physical object."
the relation of sense-data to physical objects.

The
"

collection of all physical objects

is

called

Thus our two questions may
(1) Is there any
such thing as matter ? (2) If so, what is its
matter."

be re-stated as follows
nature

:

?

The philosopher who

first brought profor regarding
forward
the
reasons
minently
the immediate objects of our senses as not

existing

independently

of us was Bishop
His Three Dialogues

Berkeley (1685-1753).
between Hylas and Philonous, in Opposition
to Sceptics and Atheists, undertake to prove
is no such thing as matter at all,
and that the world consists of nothing but
minds and their ideas. Hylas has hitherto
believed in matter, but he is no match for
Philonous, who mercilessly drives him into

that there

APPEARANCE AND REALITY
and paradoxes,

contradictions
his

as

own
it

if

19

and makes

denial of matter seem, in the end,

were almost

common

sense.

The

arguments employed are of very different
some are important and sound,
value
:

others

are

confused

or

quibbling.

But

Berkeley retains the merit of having shown
that the existence of matter is capable of
being denied without absurdity, and that if
there are any things that exist independently
of us
of

they cannot be the immediate objects

our sensations.

There are two different questions involved
when we ask whether matter exists, and it is
important to keep them clear. We commonly
mean by " matter " something which is
"
mind," something which we
opposed to
think of as occupying space and as radically
incapable of any sort of thought or consciousIt is chiefly in this sense that Berkeley
ness.
denies matter

;

that

is

to say, he does not

deny that the sense-data which we commonly
take as signs of the existence of the table are
really signs of the existence of something inde-

pendent of

us,

but he does deny that this some^

THE PROBLEMS OF PHILOSOPHY

20

thing is non-mental, that
nor ideas entertained by

it is

neither

mind

some mind.

He

admits that there must be something which
continues to exist when we go out of the room
or shut our eyes,

and that what we

call

seeing the table does really give us reason

something which persists
even when we are not seeing it. But he
thinks that this something cannot be radi-

for

believing

in

cally different in nature

from what we see, and

cannot be independent of seeing altogether,
though it must be independent of our seeing.

"
"
real
table as
thus led to regard the
God.
Such
an idea
of
mind
the
an idea in

He

is

has the required permanence and independence
of ourselves, without being as matter would



otherwise

be — something

in the sense that

can never be directly
of

quite unknowable,

we can only

and
and immediately aware
infer

it,

it.

Other philosophers since Berkeley

have

also held that, although the table does not

depend for its existence upon being seen by
me, it does depend upon being seen (or
otherwise apprehended in sensation) by some

APPEARANCE AND REALITY

21



mind not necessarily the mind of God,
but more often the whole collective mind of
the universe.

This they hold, as Berkeley

does, chiefly because they think there can




be

nothing real or at any rate nothing
known to be real except minds and their
thoughts and feelings. We might state the

argument by which they support their view
"
in some such way as this
Whatever
can be thought of is an idea in the
:

mind

of the person thinking of

it

;

therefore

nothing can be thought of except ideas in

minds

;

ceivable,

therefore

and what

anything
is

else

is

incon-

inconceivable cannot

exist."

Such an argument, in my opinion, is
and of course those who advance
it do not put it so
But
shortly or so crudely.
whether valid or not, the argument has been

fallacious

;

very widely advanced in one form or another

and

;

philosophers, perhaps a
have
held
that there is nothing real
majority,
except minds and their ideas. Such philo-

very

many

sophers are called

come

"

idealists."

When

they

to explaining matter, they either say,

22

THE PROBLEMS OF PHILOSOPHY

like Berkeley,

that matter

is

really nothing
but a collection of ideas, or they say, like

Leibniz (1646-1716), that what appears as
matter is really a collection of more or less

rudimentary minds.

But these philosophers, though they deny
matter as opposed to mind, nevertheless, in
another sense, admit matter. It will be
remembered that we asked two questions
namely,
so,

;

(1) Is there a real table at all ? (2) If

what

sort

of

object can

be

it

?

Now

both Berkeley and Leibniz admit that there
is a real table, but Berkeley says it is certain
ideas in the mind of God, and Leibniz says
it is a
colony of souls. Thus both of them

answer our

question in the affirmative,
and only diverge from the views of ordinary mortals in their answer to our second
question.

first

In

almost

fact,

all

seem to be agreed that there

is



—may

currence

depend upon
is

a

independently

sign
of

:

however much

they almost all agree that,
our sense-data colour, shape,
etc.

philosophers

a real table

of

us,

us,

smoothness,

yet

something
something

their

oc-

existing
differing,

APPEARANCE AND REALITY

23

completely from our sense-data,
and yet to be regarded as causing those
sense-data whenever we are in a suitable
perhaps,

relation to the real table.

Now

obviously this point in which the
philosophers are agreed the view that there
is





a real table, whatever

its

nature

may

be

vitally important, and it will be worth
while to consider what reasons there are for
is

accepting this view before we go on to the
further question as to the nature of the real

Our next

table.

concerned with
that there

is

chapter, therefore, will be
the reasons for supposing

a real table at

all.

will be well to
Before we go farther
consider for a moment what it is that we
it

have discovered so
that,
sort

far.

It

has

appeared

we take any common object of the
that is supposed to be known by the
if

what the senses immediately tell us
not the truth about the object as it is
apart from us, but only the truth about
senses,

is

certain sense-data which, so far as

we can

depend upon the relations between us
and the object. Thus what we directly see
see,

THE PROBLEMS OF PHILOSOPHY

24

"
merely
appearance," which we
"
"
believe to be a sign of some
reality
behind. But if the reality is not what

and

feel is

have we any means of knowing

appears,

any reality at all ? And if
have we any means of finding out what

whether there
so,

it is

is

like ?

Such questions are bewildering, and it is
difficult to know that even the strangest
hypotheses may not be true. Thus our
familiar table,

which has

roused but the

slightest thoughts in us hitherto, has

a

problem

full

of

surprising

become

possibilities.

The one thing we know about it is that it
is not what it seems.
Beyond this modest
the most complete
we
have
so
far,
result,
liberty
is

it

Leibniz

conjecture.

;

science,
is

of

scarcely

less

a vast collection

wonderful,
of

electric

us

it

tells

us

tells

a community of souls
Berkeley
God
is an idea in the mind of

;

tells

sober
us

it

charges in

violent motion.

these surprising possibilities, doubt
suggests that perhaps there is no table at all.
Philosophy, if it cannot answer so many

Among

APPEARANCE AND REALITY
questions as

power
the

of

we could

asking

interest

of

25

wish, has at least the

questions which increase
the world, and show the

strangeness and wonder lying just below the
surface even in the commonest things of
daily

life.

CHAPTER

II

THE EXISTENCE OF MATTER
In

this chapter

we have

to ask ourselves

any sense at all, there is such a
thing as matter. Is there a table which
has a certain intrinsic nature, and continues
whether, in

to exist

when

I

am

not looking, or

is

the table

merely a product of my imagination, a dreamtable in a very prolonged dream ? This
question
if

is

of the greatest importance.

we cannot be

sure

of

For

the independent

existence of objects, we cannot be sure of
the independent existence of other people's
bodies, and therefore still less of other people's

minds, since we have no grounds for believing in their minds except such as are
derived from observing their bodies. Thus
sure of the independent
if we cannot be
existence of objects,

we
36

shall be left alone

THE EXISTENCE OF MATTER
a

in

desert



outer world

that

we

be that

whole

the

nothing but a dream, and
This is an uncomfort-

is

alone exist.

but although it cannot be
proved to be false, there is not the

able possibility
strictly

may

it

27

;

slightest reason to suppose that

In this chapter we have to see

it

is

why

true.

this is

the case.

we embark upon doubtful matters,
us try to find some more or less fixed point
from which to start. Although we are
Before

let

doubting the physical existence of the table,
we are not doubting the existence of the
sense-data which

made

us think there was a

we

are not doubting that, while we
look, a certain colour and shape appear to
table

us,

;

and while we

hardness

which

is

question.

is

press, a certain sensation of

experienced

psychological,

In

fact,

we

by

us.

All

this,

are not calling in

whatever

else

may

be

some at least of our immediate
experiences seem absolutely certain.
doubtful,

Descartes

(1596-1650),

the

founder

of

modern philosophy, invented a method which
may still be used with profit the method of



28

THE PROBLEMS OF PHILOSOPHY

systematic doubt.

He determined

that he

would believe nothing which he did not see
quite clearly and distinctly to be true. Whatever he could bring himself to doubt, he would
doubt, until he saw reason for not doubting

applying this method he gradually
became convinced that the only existence of

it.

By

which he could be quite certain was his own.
He imagined a deceitful demon, who presented

unreal

things

to

his

senses

in

a

might be very
perpetual phantasmagoria
improbable that such a demon existed, but
;

still

it

was

possible,

it

and therefore doubt

by the senses
was possible.
But doubt concerning his own existence
was not possible, for if he did not exist, no

concerning things perceived

demon could
he must exist

deceive him.
;

if

If

he doubted,

he had any experiences

whatever, he must exist. Thus his own existence was an absolute certainty to him.
"
I think, therefore I am," he said {Cogiio,
ergo

sum)

;

and on the

basis of this certainty

he set to work to build up again the world
of knowledge which his doubt had laid in

THE EXISTENCE OF MATTER

29

inventing the method of doubt,
and by showing that subjective things are
the most certain, Descartes performed a

By

ruins.

great service to philosophy, and one which
makes him still useful to all students of

the subject.

But some care

"

cartes'

am "

needed in using Des-

is

argument.

/ think, therefore /

says rather more than

tain.

is

strictly cer-

might seem as though we were

It

quite sure of being the same person to-day
as we were yesterday, and this is no doubt
true

in

some

But the

sense.

Self

real

is

as hard to arrive at as the real table, and

does not seem to have that absolute, convincing certainty that belongs to particular

When

experiences.
see a certain

brown

tain at once

is

not

colour," but rather,

This

seen."

of

I look at

colour,

"
"

/

my

what

am

is

table

seeing a

a brown colour

course

involves

and

quite cer-

is

brown
being

something

somebody) which (or who) sees the brown
but it does not of itself involve that
more or less permanent person whom we call
(or

colour

"

I.'-

;

So

far as

immediate certainty goes.

30
it

THE PROBLEMS OF PHILOSOPHY
be

might

that

the

something which

brown colour is quite momentary,
and not the same as the something which
has some different experience the next
moment.
Thus it is our particular thoughts and
sees the

have primitive certainty. And
this applies to dreams and hallucinations as
when we
well as to normal perceptions
feelings that

:

dream or

we certainly do have
we think we have, but for

see a ghost,

the sensations

is held that no physical
to
these sensations. Thus
object corresponds

various reasons

it

the certainty of our knowledge of our own
experiences does not have to be limited in

any way to allow
therefore,
solid basis
of

for exceptional cases.

we have,

for

what

it is

Here,

worth, a

from which to begin our pursuit

knowledge.

The problem we have to consider is this
Granted that we are certain of our own sensedata, have we any reason for regarding them
:

as signs of the existence of something else,
which we can call the physical object? When

we have enumerated

all

the sense-data which

THE EXISTENCE OF MATTER

81

we should naturally regard as connected with
the table, have we said all there is to say
about the table, or is there still something
else
something not a sense-datum, some-



thing which persists when we go out of the
room? Common sense unhesitatingly answers

What can

be bought and sold
and pushed about and have a cloth laid on it,
and so on, cannot be a mere collection of sensethat there

is.

data.

If

the

table,

we

shall

cloth

completely

hides

the

derive no sense-data from

the table, and therefore,

if

the table were

it would have ceased to
and the cloth would be suspended in

merely sense-data,
exist,

air, resting, by a miracle, in the place
where the table formerly was. This seems
but whoever wishes to beplainly absurd

empty

;

come a philosopher must
frightened by absurdities.
One great reason why it is

learn not to be

felt

that

we must

secure a physical object in addition to the
sense-data, is that we want the same object
for different people.
When ten people are

round a dinner-table, it seems preposterous to maintain that they are not
sitting

32

THE PROBLEMS OF PHILOSOPHY

seeing the same tablecloth, the same knives
and forks and spoons and glasses. But the

sense-data are private to each separate person ;
what is immediately present to the sight

not immediately present to the
they all see things from
sight of another

of one

is

:

slightly different points of view,

see

them

slightly differently.

and therefore

Thus,

if

there

are to be public neutral objects, which can be
in some sense known to many different people,

must be something over and above the
private and particular sense-data which ap-

there

pear to various people.

What

reason, then,

have we for believing that there are such
public neutral objects ?
The first answer that naturally occurs to

one

is

that, although different people

see the table slightly differently,

still

may

they

all

more or less similar things when they
look at the table, and the variations in what
they see follow the laws of perspective and
reflection of light, so that it is easy to arrive
see

at a

permanent object underlying all the different people's sense-data. I bought my table
from the former occupant of my room ; I

THE EXISTENCE OF MATTER

33

could not buy his sense-data, which died
when he went away, but I could and did buy
the confident expectation of more or less
similar sense-data.
Thus it is the fact that

have similar sense-data, and
that one person in a given place at different
times has similar sense-data, which makes
different people

us suppose that over and above the sensedata there is a permanent public object which
underlies or causes the sense-data of various

people and various times.
Now in so far as the above considerations

depend upon supposing that there are other
people besides ourselves, they beg the very
question at issue. Other people are repre-

sented to

me by

certain sense-data, such as

them or the sound of their voices,
had no reason to believe that there

the sight of

and

if

I

were physical objects independent of my
sense-data, I should have no reason to believe
that other people exist except as part of my
dream. Thus, when we are trying to show that

must be objects independent of our own
sense-data, we cannot appeal to the testimony

there

of other people, since this testimony itself

B

34

THE PROBLEMS OF PHILOSOPHY

consists of sense-data,

and does not reveal

other people's experiences unless our own
sense-data are signs of things existing inde-

oendently

of

us.

in

We
our

must

therefore,

if

own

find,
purely private
experiences, characteristics which show, or
tend to show, that there are in the world

possible,

things other than ourselves and our private

experiences.
In one sense

it

must be admitted that we

can never prove the existence of things other
than ourselves and our experiences. No

from the hypothesis
that the world consists of myself and my

logical absurdity results

thoughts and feelings and sensations, and
that everything else is mere fancy. In

dreams a very complicated world may seem
to be present, and yet on waking we find it
was a delusion

;

that

is

to say,

we

find that

the sense-data in the dream do not appear to
have corresponded with such physical objects
as

we should

data.

world

(It
is

is

naturally infer from our sensetrue that, when the physical

assumed,

it is

possible to find physical

causes for the sense-data in dreams

:

a door

THE EXISTENCE OF MATTER

35

banging, for instance, may cause us to dream
But although, in
of a naval engagement.
this case, there is a physical cause for the

not a physical object
in the way in
sense-data
corresponding to the
which an actual naval battle would correthere

sense-data,

is

spond.) There is no logical impossibility in
the supposition that the whole of life is a

dream, in which we ourselves create

all

the

come before us. But although
not logically impossible, there is no
reason whatever to suppose that it is true
objects that
this is

;

and

it

in fact, a less simple hypothesis,

is,

viewed as a means of accounting for the
facts of our own life, than the common-sense
hypothesis that there really are objects independent of us, whose action on us causes our
sensations.

The way in which
supposing

that

simplicity

there

comes

in

from

are

physical
the
cat
appears at
objects
one moment in one part of the room, and at
another in another part, it is natural to
is

easily seen.

suppose that

it

has

really

If

moved from the one

to

the other, passing over a series of intermediate

THE PROBLEMS OF PHILOSOPHY

36

But if it is merely a set of sensehave ever been in any place
cannot
data,
thus we shall have
where I did not see it
to suppose that it did not exist at all while
positions.
it

;

I

was not looking, but suddenly sprang

being

in

whether

a

new

If

place.

I see it or not,

into

the cat exists

we can understand

from our own experience how it gets hungry
but if it
between one meal and the next
;

does not exist when I

am

not seeing it, it
should
that
seems odd
grow during
appetite
non-existence as fast as

during existence.
consists
the
cat
And
only of sense-data, it
cannot be hungry, since no hunger but my
if

own can be

a sense-datum to me.

Thus

the behaviour of the sense-data which represent the cat to me, though it seems quite
natural

when regarded

as

an expression

of

hunger, becomes utterly inexplicable when
regarded as mere movements and changes
of patches of colour, which are as incapable
of

hunger as a triangle

is

of playing foot-

ball.

But the

difficulty in the case of the cat is

nothing compared to the difTiculty in the case

THE EXISTENCE OF MATTER
of

human

When human

when we hear

beings speak
certain noises which

associate with ideas,

and simultaneously

—that
we

37

is,

beings.

see certain motions of lips and expressions of
face it is very difficult to suppose that what



we hear is not the expression of a thought,
as we know it would be if we emitted the
same sounds. Of course similar things happen
in dreams, where we are mistaken as to the
existence of other people. But dreams are

more or less suggested by what we call waking
more or less
life, and are capable of being
accounted for on scientific principles if we
assume

that

there

really

is

a

physical

Thus every
simplicity
that
natural
the
us
to
view,
adopt
urges
our
than
other
there really are objects
principle of

world.

selves

and our sense-data which have an

existence not dependent

upon our perceiving

them.
not by argument that we
originally come by our belief in an independent
We find this belief ready
external world.
in ourselves as soon as we begin to reflect

Of course

it is

:

it is

what may be

called

an

instinctive belief

THE PROBLEMS OF PHILOSOPHY

38

We

should never have been led to question
this belief but for the fact that, at any rate
in the case of sight, it seems as if the sense-

were instinctively believed to
be the independent object, whereas argument
shows that the object cannot be identical

datum

itself

This discovery, hownot at all paradoxical in the

with the sense-datum.

ever—which

case of taste

is

and smell and sound, and only
touch

slightly so in the case of

—leaves

un-

diminished our instinctive belief that there
are objects corresponding to our sense-data.
Since this belief does not lead to any diffi-

but on the contrary tends to simplify
and systematise our account of our experi-

culties,

no good reason for rejecting
We may therefore admit though with
it.
a slight doubt derived from dreams that
the external world does really exist, and is not
ences, there seems



wholly dependent for

its

continuing to perceive

it.

existence

The argument which has
clusion

is

wish, but



upon our

led us to this con-

doubtless less strong than

we could

typical of many philosophical
to
arguments, and it is therefore worth while
it is

THE EXISTENCE OF MATTER

39

and
All knowledge, we find, must be
validity.
built up upon our instinctive beliefs, and if
these are rejected, nothing is left. But among
our instinctive beliefs some are much stronger
than others, while many have, by habit and

consider

briefly

character

general

become entangled with other

association,
beliefs,

its

not

really

supposed to be

but

instinctive,

part

of

what

is

falsely

believed

instinctively.

Philosophy should show us the hierarchy
of our instinctive beliefs, beginning with
those we hold most strongly, and presenting
each as

much

isolated

and as

vant additions as possible.
care to

show

that, in the

free

from

irrele-

It should take

form

in

which they

are finally set forth, our instinctive beliefs

but form a harmonious system.
There can never be any reason for rejecting

do not

clash,

one instinctive belief except that it clashes
with others thus, if they are found to harmonise, the whole system becomes worthy of
;

acceptance.
It is of course possible that
beliefs

may

all

or

any

of our

be mistaken, and therefore

all

40

THE PROBLEMS OF PHILOSOPHY

ought to be held with at least some
element of doubt. But we cannot
reason

to
of

ground

reject

some

a

belief

other

except

belief.

slight

on

have
the

Hence, by

organising our instinctive beliefs and their

consequences, by considering which

them

is

it

modify

most

possible,

if

necessary, to

abandon, we can

or

the basis

of

what we

instinctively

accepting

as

among

our

believe,

arrive,
sole

at

an

on
data
or-

derly systematic organisation of our knowledge, in which, though the possibility of
error remains,

its likelihood is diminished
the
interrelation
of the parts and by
by
the critical scrutiny which has preceded

acquiescence.

This function, at least, philosophy can perform. Most philosophers, rightly or wrongly,
believe that philosophy can do

than
not

this

— that

it

much more

can give us knowledge,

otherwise

attainable, concerning the
universe as a whole, and concerning the nature
of ultimate reality.
Whether this be the

case or not, the

spoken

of

more modest function we have

can certainly be performed by

THE EXISTENCE OF MATTER

41

philosophy, and certainly suffices, for those
to doubt the adequacy

who have once begun
of

common

difficult

involve.

sense, to justify the

arduous and

labours that philosophical problems

CHAPTER

III

THE NATURE OF MATTER
preceding chapter we agreed,
though without being able to find demonstrative reasons, that it is rational to believe that

In

the

our sense-data
regard

as

really

signs

—for example, those which we
with

associated
of

my

table

—are

the existence of something
and our perceptions. That

independent of us
is

and above the sensations of
hardness, noise, and so on, which

to say, over

colour,

make up

the appearance of the table to
me, I assume that there is something else,
are
appearances.
of which these things

The colour

ceases to exist

eyes, the sensation of
exist

if

I

remove

if

I

shut

my

hardness ceases to

my arm

from contact

with the table, the sound ceases to exist if
I cease to rap the table with my knuckles.
42

THE NATURE OF MATTER
But

I

things

do not believe that when
the

cease

table

43
these

all

On

ceases.

the

contrary, I believe that it is because the
table exists continuously that all
these

when

sense-data will reappear
replace

eyes,

to

rap with

my
my knuckles.

we have

to

What

is

the

which

persists

ception of

To

and

arm,

consider in

nature

of

my

open

begin

again

The question

this

chapter

this

real

independently

of

is

table,

my

per-

this question physical science gives

still

:

it ?

answer, somewhat incomplete
part

I

it is

true,

and

an
in

very hypothetical, but yet deserving

of respect so far as it goes.

Physical science,
more or less unconsciously, has drifted into
the view that all natural phenomena ought to

be reduced to motions.

Light and heat and

sound are all due to wave-motions, which
from the body emitting them to the

travel

person
sound.

who

sees light or feels heat or hears

That which has the wave-motion

either cether or

case

is

"

is

gross matter," but in either

what the philosopher would call matter.

The only properties which

science assigns to

THE PROBLEMS OF PHILOSOPHY

44

are position in space, and the povyer of
motion according to the laws of motion.

it
I

1

Science does not deny that

may have

it

other

properties ; but if so, such other properties
are not useful to the man of science, and in

no way
mena.
It

is

him

assist

in explaining the

sometimes said that "

of wave-motion," but this

is

pheno-

light is a

form

misleading, for

the light which we immediately

see,

which

we know
is

directly by means of our senses,
not a form of wave-motion, but some-

thing

different

quite

we all know if we
we cannot describe

— something

which

are not blind, though
it so as to convey our

knowledge to a man who is blind. A wavemotion, on the contrary, could quite well
be

described to

can

a

blind

man,

a

he

since

of

acquire
knowledge
space by
the sense of touch
and he can experience
a wave-motion by a sea voyage almost
;

as

well

blind

as

man

mean by

we

can.

But

can understand,

light:

which a blind

we mean by

man

this,
is

which

a

not what we

light just

that

can never understand,

THE NATURE OF MATTER
and

which

we

can

never

45

describe

to

him.

Now this something,

which

all of

us

who

are

not blind know, is not, according to science,
it is
really to be found in the outer world
:

something caused by the action of certain

waves upon the eyes and nerves and brain

of

the person who sees the light.
When it is
said that light is waves, what is
really
meant is that waves are the physical cause
of our sensations of light.

But

light itself,

thing which seeing people experience
and blind people do not, is not supposed by

the

science to form

any part of the world that
us and our senses.
And
remarks would apply to other

independent of

is

very similar
kinds of sensations.

It is not only colours

and sounds and so
on that are absent from the scientific world
of matter, but also space as we get it
through
sight or touch.

It

is

essential to science that

matter should be in a space, but the
space in which it is cannot be exactly the

its

space
as

we

we

see or feel.

see it

is

To begin

v/ith, space
not the same as space as we

46
get

THE PROBLEMS OF PHILOSOPHY
it

of touch

by the sense

experience in infancy that

it

;

we

is

learn

only by

how

to

touch things we see, or how to get a sight
of things which we feel touching us.
But
the

space

of

science

is

neutral

as

be-

tween touch and sight
thus it cannot be
either the space of touch or the space of
;

sight.

Again, different people see the same object
as

of

different

shapes,

according to

their

point of view. A circular coin, for example,
though we should always judge it to be
circular,

will

oval

look

straight in front of

unless

we

are

When we

judge that
it is circular, we are judging that it has a
real shape which is not its apparent shape,

but belongs to

it.

it

intrinsically

apart from

appearance. But this real shape, which
what concerns science, must be in a real
space, not the same as anybody's apparent
The real space is public, the apparent
space.

its
is

space is private to the percipient. In different people's private spaces the same object
seems to have different shapes thus the real
;

space, in which

it

has

its real

shape,

must be

THE NATURE OF MATTER
different

from the private spaces.

of science, therefore,

47

The space

'

though connected with

the spaces we see and feel, is not identical
with them, and the manner of its connection,
'

requires investigation.

We

agreed provisionally that physical
objects cannot be quite like our sense-data,
but may be regarded as causing our sensations.

These physical objects are in the
which we may call " physi-

space of science,

"

It is important to notice that,
space.
our sensations are to be caused by physical objects, there must be a physical space

cal
if

containing

these

and

objects

our

sense-

organs and nerves and brain. We get a
sensation of touch from an object when

we are in
when some

contact with
part of our

it

;

that

is

to say,

body occupies a place

in physical space quite close to the space
see an object
occupied by the object.

We

speaking) when no opaque body
between the object and our eyes in phy-

(roughly
is

sical space.
Similarly, we only hear or smell
or taste an object when we are sufficiently
near to it, or when it touches the tongue.

48
or

THE PROBLEMS OF PHILOSOPHY
has

some

suitable

position in physical
our
to
space relatively
body. We cannot
begin to state what different sensations
we shall derive from a given object under
different circumstances unless

object and our body as both

we regard the
in one physical

space, for it is mainly the relative positions
of the object and our body that determine

what sensations we

shall

derive

from the

object.

Now

our sense-data are situated in our

private spaces, either the space of sight or
the space of touch or such vaguer spaces
as other senses may give us.
If, as science

and common sense assume, there

is

one

public all-embracing physical space in which
physical objects are, the relative positions of

physical objects in physical space must more
or less correspond to the relative positions of

sense-data in our private spaces. There is
no difficulty in supposing this to be the case.
If we see on a road one house nearer to us
than another, our other senses will bear
out the view that it is nearer ; for example,
it

will

be reached sooner

if

we walk along

THE NATURE OF MATTER

49

Other people will agree that the
house which looks nearer to us is nearer ;

the road.

the ordnance

map

will

take the same view

;

and thus everything points to a spatial
relation between the houses corresponding
to the relation between the sense-data which

we

when we look at the houses. Thus we
assume
that there is a physical space
may
in which physical objects have spatial resee

corresponding to those which the
corresponding sense-data have in our private
lations

spaces.

dealt

It

is

this physical

with in

space which

geometry and

physics and astronomy.
Assuming that there

is

assumed

physical

is

in

space,

and that it does thus correspond to private
We
spaces, what can we know about it ?
can know only what

is required in order to
secure the correspondence.
That is to say,

we can know nothing of what it is like in itself,
but we can know the sort of arrangement
of physical objects

spatial relations.

which

results

We can know,

that the earth and

from their

for example,

moon and sun

one straight line during an

eclipse,

are in

though

50

THE PROBLEMS OF PHILOSOPHY

we cannot know what a physical straight
line is in itself, as we know the look of a
Thus we
straight line in our visual space.
come to know much more about the relations of distances in physical space than
about the distances themselves; we may

know

that

one

another, or that

distance
it is

line as the other,

is

greater

than

along the same straight

but we cannot have that

immediate acquaintance with physical distances that we have with distances in our
private spaces, or with colours or sounds
or other sense-data. We can know all those
things about physical space which a man
born blind might know through other people

but the kind of
about the space of sight
things which a man born blind could never
;

know about the space
know about physical

of sight

we

space.

We

also cannot

can know

the properties of the relations required to
preserve the correspondence with sense-data,

but we cannot know the nature of the terms

between which the relations hold.

With regard

to time, our feeling of dura-

tion or of the lapse of time

is

notoriously an

THE NATURE OF MATTER

51

unsafe guide as to the time that has elapsed
by the clock. Times when we are bored or
suffering pain pass

times

slowly,

when we

are agreeably occupied pass quickly, and
times when we are sleeping pass almost as
if they did not exist.
Thus, in so far as time
is

constituted

by duration, there

is

the same

necessity for distinguishing a public and a
private time as there was in the case of

But

space.

an order
to

so

in

of before

make such a

far

and

as time consists

after, there is

distinction

which events seem to have

;

in

no need

the time-order
is,

so far as

we

can see, the same as the time-order which
they do have. At any rate no reason can
be given for supposing that the two orders are
not the same. The same is usually true of
a regiment of men are marching
along a road, the shape of the regiment will
look different from different points of view,
space

:

but the

same

if

men

order

will

from

we regard the

all

appear arranged in the
points of view.

Hence

order as true also in physical

space, whereas the shape is only supposed
to correspond to the physical space so far

THE PROBLEMS OF PHILOSOPHY

52
as

required for the preservation of the

is

order.

In saying that the time-order which events
seem

have

to

which they

is

the same as the time-orier

have, it is necessary to
a
possible misunderstanding.
guard against
It must not be supposed that the various

states

of

the same

really

physical objects have
time-order as the sense-data which
different

constitute the perceptions of those objects.
Considered as physical objects, the thunder

and

lightning

are

simultaneous

to say, the lightning
the disturbance of the

is

;

that

is

simultaneous with

air in the place
the
disturbance
where
begins, namely, where
the lightning is. But the sense-datum

which we

call

Similarly,

it

hearing the thunder does not
take place until the disturbance of the air
has travelled as far as to where we are.
takes about eight minutes for

the sun's light to reach us thus, when we
see the sun we are seeing the sun of eight
;

minutes

ago.

So

far

as

our

sense-data

afford evidence as to the physical sun they
afford evidence as to the physical sun of

THE NATURE OF MATTER

53

if the physical sun had
eight minutes ago
ceased to exist within the last eight minutes,
;

that would

which

data

make no difference to the sensewe call " seeing the sun."

This affords a fresh illustration of the necesof

sity

distinguishing

and physical

between sense-data

objects.

What we have found as regards
much the same as what we find in

space

is

relation

to the correspondence of the sense-data with
their

physical counterparts.
looks blue and another red,

If

one object

we may

reason-

ably presume that there is some corresponding
difference between the physical objects ; if
two objects both look blue, we may presume
a corresponding similarity. But we cannot
hope to be acquainted directly with the
quality in the physical object which makes
Science tells us that
it look blue or red.
this

is

quality

motion, and

a

certain

sort

of

wave-

sounds familiar, because
we think of wave-motions in the space we
be

no

wave-motions must really
physical space, with which we have

But

see.

in

this

direct

the

acquaintance

;

thus

the

real

54

THE PROBLEMS OF PHILOSOPHY

wave - motions have not that f amiharity
which we might have supposed them to
have. And what holds for colours is closely
similar to what holds for other sense-data.
Thus we find that, although the relations
of physical objects have all sorts of knowable

properties,

derived from

their corre-

spondence with the relations of sense-data,
the physical objects themselves remain un-

known

in their intrinsic nature, so far at least

by means of the senses.
The question remains whether there is any
other method of discovering the intrinsic
as can be discovered

nature of physical objects.

The most natural, though not ultimately
the most defensible, hypothesis to adopt in the
any rate as regards visual
sense-data, would be that, though physical
objects cannot, for the reasons we have been

first

instance, at

considering,

they

may

be exactly like sense-data, yet

be more or

less like.

According to

this view, physical objects will, for example,

have colours, and we might, by good
luck, see an object as of the colour it really
is.
The colour which an object seems to
really

THE NATURE OF MATTER

55

have at any given moment will in general
be very similar, though not quite the same,
from many different points of view we might
"
" colour to be a sort
real
thus suppose the
of medium colour, intermediate between
;

the various shades which appear from the
different points of view.

perhaps not capable of
being definitely refuted, but it can be shown
to be groundless. To begin with, it is plain

Such a theory

is

we see depends only upon the
nature of the light-waves that strike the eye,
and is therefore modified by the medium

that the colour

intervening between us and the object, as
well as by the manner in which light is reflected

from the object in the direction of

the eye.
unless it

The intervening
is

air alters colours

and any strong
them completely. Thus

perfectly clear,

reflection will alter

we see is a result of the ray as it
the
reaches
eye, and not simply a property
of the object from which the ray comes.
Hence, also, provided certain waves reach

the colour

the eye, we shall see a certain colour, whether
the object from which the waves start has

THE PROBLEMS OF PHILOSOPHY

56

any colour or
tuitous

have

to

Thus

not.

suppose

and

colours,

it

is

physical objects
therefore there is no

making such a

justification for

Exactly similar

quite gra-

that

arguments

supposition.

will

apply

to

other sense-data.
It remains to ask

whether there are any
general philosophical arguments enabling us
to say that, if matter is real, it must be of
such and such a nature. As explained above,
,

very

philosophers, perhaps most, have

many

held that whatever

is

real

must be

in

some

sense mental, or at any rate that whatever

we can know anything about must be
'

sense mental.
*'

idealists."

in

some

Such philosophers are called
what ap-

Idealists tell us that

pears as matter

is

really

something mental

;

namely, either (as Leibniz held) more or less
rudimentary minds, or (as Berkeley contended)
ideas in the

monly

say,

idealists

minds which, as we should com"
"
the matter. Thus
perceive

deny the existence

of

matter as

from mind,
something
though they do not deny that our sense-data
are signs of something which exists indeintrinsically different

THE NATURE OF MATTER
pendently of our private sensations.
chapter we

following
the reasons

—in

my

shall

57

In the

consider briefly



opinion fallacious
which idealists advance in favour of their
theory.

CHAPTER

IV

IDEALISM

The word
philosophers

We

shall

whatever
be

"

idealism

in

"

is

somewhat

understand by

it

to exist,

different

senses,.

the doctrine thai;
rate whatever can.

exists, or at

known

used by different

any
must be

in

some

senses

This doctrine, which is very widely
held among philosophers, has several forms,.

mental.

and is advocated on several
The doctrine is so widely
teresting

in

itself,

that

different grounds.

held,

and

so in"

even the briefest

survey of philosophy must give some account of it.

Those who are unaccustomed to philosophical speculation may be inclined to
dismiss such a doctrine as obviously absurd.
There is no doubt that common sense regards
tables and chairs and the sun and moon and
68

IDEALISM

59

material objects generally as something radicand the contents of
ally different from minds

minds, and as having an existence which
might continue if minds ceased. We think

matter as having existed long before there
were any minds, and it is hard to think of it
But
as a mere product of mental activity.
be
is
not
to
idealism
or
true
whether
false,
of

dismissed as obviously absurd.
We have seen that, even if physical objects

)

do have an independent existence, they must
differ very widely from sense-data, and can
only have a correspondence with sense-data,
in the same sort of way in which a catalogue
has a correspondence with the things catalogued.

Hence

common

sense

leaves

us

completely in the dark as to the true intrinsic
nature of physical objects, and if there were

good reason to regard them as mental, we
not legitimately reject this opinion
merely because it strikes us as strange. The
truth about physical objects must be strange.

could

It

may be unattainable, but if any

believes that he has attained

what he

it,

philosopher
the fact that

offers as the truth is strange

ought

\

THE PROBLEMS OF PHILOSOPHY

60

made a ground

not to be

of objection to his

opinion.

The grounds on which ideahsm

is

advocated

are generally grounds derived from the theory
of knowledge, that is to say, from a discussion

which things must satisfy
in order that we may be able to know them.
of the conditions

The

first

serious attempt to establish idealism

on such grounds was that of Bishop Berkeley.
He proved first, by arguments which were
largely valid, that our sense-data cannot be
supposed to have an existence independent

"

"

in
but must be, in part at least,
the mind, in the sense that their existence
would not continue if there were no seeing

of us,

or hearing or touching or smelling or tasting.
So far, his contention was almost certainly

even if some of his arguments were not
But he went on to argue that sense-data

valid,
so.

were the only things of whose existence our
perceptions could assure us, and that to be
"

"

a mind, and therefore
Hence he concluded that
nothing can ever be known except what is in
some mind, and that whatever is known

known
to

be

is

to be

mental.

in

IDEALISM

my mind

without being in
other mind.

61

must be

in

some

In order to understand his argument, it is
necessary to understand his use of the word
"
"
"
idea." He gives the name
idea
to anything which is immediately known, as, for
example, sense-data are known. Thus a particular colour which we see is an idea so is
;

a voice which we hear, and so on. But the
term is not wholly confined to sense-data.

There

be things remembered or
we have

also

will

imagined, for with such things also

immediate acquaintance at the moment of

remembering or imagining.
mediate data he

He

calls

then

"

All

ceive

all

"

im-

ideas."

to

consider
proceeds
such
as
a
for
instance.
tree,
objects,

that

such

common
He shows

we know immediately when we "

per-

the tree consists of ideas in his sense

and he argues that there is not
the slightest ground for supposing that there
is anything real about the tree except what is
of the word,

perceived.

Its

being perceived
"
"

men its

esse

he says, consists in
in the Latin of the school-

being,
:

is

"
percipi.^'

He fully admits

\

i

1

62

THE PROBLEMS OF PHILOSOPHY

that the tree must continue to exist even

we shut our eyes
near

it.

says,

is

But

or

when
when no human being is

continued existence, he
due to the fact that God continues to
"
"
the
real
perceive it
tree, which corresponds to what we called the physical object,
this

;

mind of God, ideas
those we have when we see

consists of ideas in the

more or

less like

the tree, but differing in the fact that they are
permanent in God's mind so long as the tree
continues

to exist.
All our perceptions,
to
him, consist in a partial partiaccording

God's

in

cipation

perceptions,

and

it

is

because of this participation that different
people see more or less the same tree. Thus
apart from minds and their ideas there is
nothing in the world, nor is it possible that
else

anything
whatever

is

known

There are in
fallacies

should ever be known, since
is

necessarily an idea.

argument a good many
which have been important in the
this

history of philosophy, and which it will be
as well to bring to light.
In the first place,

there
of the

is

a confusion engendered by the use
We think of an idea

word " idea."

IDEALISM

63

something in somebody's mind,

as essentially

and thus when we are told that a tree
entirely of ideas,
if so,

it is

consists

natural to suppose that,

the tree must be entirely in minds. But
"
"
in
the mind is am-

the notion of being

We

speak of bearing a person in
mind, not meaning that the person is in our
minds, but that a thought of him is in our
biguous.

minds.

When

a

man

says that some business

he had to arrange went clean out of his mind,
he does not mean to imply that the business
itself was ever in his mind, but only that a
thought of the business was formerly in his
mind, but afterwards ceased to be in his

mind.
tree

And

must be

so

when Berkeley says that the
minds if we can know it,

in our

that he really has a right to say is that a
thought of the tree must be in our minds. To
all

argue that the tree itself must be in our minds
like arguing that a person whom we bear

is

in

mind

is

himself in our minds.

This con-

fusion may seem too gross to have been really
committed by any competent philosopher,

but various attendant circumstances rendered
it

possible.

In order to see how

it

was

THE PROBLEMS OF PHILOSOPHY

64

possible,

we must go more deeply

into the

question as to the nature of ideas.

Before taking up the general question of
the nature of ideas, we must disentangle two
entirely separate questions

which

arise con-

cerning sense-data and physical objects. We
saw that, for various reasons of detail,

Berkeley was right in treating the sense-data
which constitute our perception of the tree
as

more or

less subjective, in

they depend upon us as
and would not exist

tree,

being

perceived.

different

the sense that

much
if

as

upon the

the tree were not

But this is an entirely
from the one by which

point
Berkeley seeks to prove that whatever can be
immediately known must be in a mind. For

purpose arguments of detail as to the dependence of sense-data upon us are useless.

this

It is necessary to prove, generally, that

by

being known, things are shown to be mental.
This is what Berkeley believes himself to
this question, and not our
to the difference between
as
previous question
sense-data and the physical object, that must

have done.

now concern

It

is

us.

IDEALISM

65

"
"
idea
in Berkeley's
Taking the word
sense, there are two quite distinct things to
be considered whenever an idea is before the

There is on the one hand the thing
which we are av/are say the colour of
my table and on the other hand the actual
mind.
of





awareness

the mental act of apprehending the thing. The mental act is undoubtedly mental, but is there any reason
itself,

to suppose that the thing apprehended is
in any sense mental ?
Our previous arguments concerning the colour did not prove
it

to be mental

;

they only proved that

its

existence depends upon the relation of our
sense organs to the physical object in our
That is to say, they proved
case, the table.



that a certain colour will exist, in a certain
light, if a normal eye is placed at a certain
point relatively to the table. They did not
prove that the colour is in the mind of the
percipient.

Berkeley's view, that obviously the colour

must be in the mind, seems to depend for

its

upon confusing the thing apprehended with the act of apprehension. Either
plausibility

o

THE PROBLEMS OF PHILOSOPHY

66

"
"
might be called an idea
probably
either would have been called an idea by
of these

;

Berkeley. The act is undoubtedly in the
mind hence, when we are thinking of the
act, we readily assent to the view that ideas
must be in the mind. Then, forgetting that
this was only true when ideas were taken
as acts of apprehension, we transfer the pro"
"
ideas are in the mind
to
position that
;

ideas in the other sense,

i.e.

to the things

apprehended by our acts of apprehension.
Thus, by an unconscious equivocation, we
arrive at the conclusion that whatever we
can apprehend must be in our minds. This
seems to be the true analysis of Berkeley's

and the ultimate

argument,

which

it

fallacy

upon

rests.

This question of the distinction between
act and object in our apprehending of things
is

vitally important, since our

of acquiring

The

knowledge

is

whole power
bound up with it.

faculty of being acquainted

main

with things

other than

itself

of a mind.

Acquaintance with objects essenbetween the mind

is

the

tially consists in a relation

characteristic

IDEALISM

67

and something other than the mind it
this that constitutes the mind's power
;

knowing things.
known must be

If

in

we say that the
the mind, we are

is

of

things
either

unduly limiting the mind's power of knowing,
or we are uttering a mere tautology. We
are uttering a mere tautology if we mean by
"
"
"
the same as by
in the mind
before the

mind," i.e. if we mean merely being apprehended by the mind. But if we mean this,
we shall have to admit that what, in this
sense, is in the mind, may nevertheless be not
mental.

Thus when we

realise the nature of

knowledge, Berkeley's argument is seen to
be wrong in substance as well as in form, and



grounds for supposing that "ideas" i.e.
the objects apprehended must be mental,
are found to have no validity whatever.

his



grounds in favour of idealism may
It remains to see whether
be dismissed.

Hence

his

there are any other grounds.
It is often said, as though

it

were a

self-

we cannot know that
which we do not know. It

evident truism, that

anything exists
is

inferred that whatever can in

any way be

68

THE PROBLEMS OF PHILOSOPHY
must be at least
whence it
being known by us

relevant to our experience

capable of
follows that

;

matter were essentially somewith
which
we could not become acthing
quainted, matter would be something which
if

we could not know to

and which could

exist,

have for us no importance whatever.
generally

also

implied,

for

reasons

It is

which

remain obscure, that what can have no importance for us cannot be real, and that
not composed of
minds or of mental ideas, is impossible and a

therefore matter,

if

it is

mere chimoera.

To go

this argument fully at our
would
be impossible, since it
present stage

into

points requiring a considerable prebut certain reasons for
liminary discussion
raises

;

argument may be noticed at
To begin at the end
there is no
once.
reason why what cannot have any practical
rejecting the

:

importance for us should not be
true that,

if

truth

It

is

theoretical

everything real
since,

real.

is

of

importance is included,
some importance to us,

persons desirous of knowing the
about the universe, we have some
as

IDEALISM
in

interest

included,

everything

But

contains.

it is

if

this

69

that
sort

universe

interest

is

not the case that matter has no

importance for us, provided
if

the
of

we cannot know that

obviously, suspect that
wonder whether it does

it

it

exists.

it

may

;

even

exists,

hence

We

can,

exist,

and

it

con-

is

nected with our desire for knowledge, and
has the importance of either satisfying or

thwarting this desire.
Again,
is

in

it

fact

is

by no means a

false,

that

we

truism,

cannot

and

know

that anything exists which we do not know.
The word " know " is here used in two differ(1) In its first use it is applicable
to the sort of knowledge which is opposed to
error, the sense in which what we know is

ent senses.

the sense which applies to our beliefs
and convictions, i.e. to what are called judgtrue,

ments.

In this sense of the word we know

something is the case. This sort of knowledge may be described as knowledge of truths.
"
know "
(2) In the second use of the word
that

above, the word applies to our knowledge of
This
things^ which we may call acquaintance.

THE PROBLEMS OF PHILOSOPHY

70
is

the sense in which

we know

sense-data.

involved
(The
roughly that
between savoir and connaitre in French, or
between wissen and kennen in German.)
Thus the statement which seemed like a
distinction

is

truism becomes, when re-stated, the following
"
We can never truly judge that something
with which we are not acquainted exists."
:

This

by no means a truism, but on the

is

contrary a palpable falsehood, I have not
the honour to be acquainted with the Emperor

but

of Russia,

It

may

be

I truly

judge that he

exists.

said, of course, that I judge this be-

cause of other people's acquaintance with him.
This, however, would be an irrelevant retort,
since,

know
him.

the principle were true, I could not
that any one else i^ acquainted with
But further there is no reason why I
if

:

should not

know of the existence of something

with which nobody
is

is

acquainted.

This point

important, and demands elucidation.
I am acquainted with a thing which

If

me the knowBut it is not true that,
conversely, whenever I can know that a

exists,

my

ledge that

acquaintance gives

it exists.

IDEALISM

71

thing of a certain sort exists, I or some one
else must be acquainted with the thing.

What

happens, in cases where I have true
judgment without acquaintance, is that the
thing is known to me
virtue of some

in

by

description,

general

and

principle,

that,

the

a thing answering to this decan
be inferred from the existence
scription
of something with which I am acquainted.

existence of

In order to understand this point fully, it
will be well first to deal with the difference

between

by acquaintance and
knowledge by description, and then to consider what knowledge of general principles,
if any, has the same kind of
certainty as our
knowledge

knowledge of the existence of our own exThese subjects will be dealt with
periences.

m the

following chapters.

CHAPTER V
KNOWLEDGE BY ACQUAINTANCE AND KNOWLEDGE BY DESCRIPTION
In the preceding chapter we saw that
there are two sorts of knowledge
knowledge
:

and knowledge of truths. In this
shall be concerned exclusively
with knowledge of things, of which in turn we
Knowshall have to distinguish two kinds.
kind
we
it
of
the
when
is
of
things,
ledge

of things,

chapter we

call

knowledge by acquaintance, is essentially
simpler than any knowledge of truths, and
logically independent of knowledge of truths,
though it would be rash to assume that human
beings ever, in fact, have acquaintance with
things without at the same time knowing

some truth about them. Knowledge of things
by description, on the contrary, always involves, as

we

shall find in the course of the
72

ACQUAINTANCE AND DESCRIPTION

78

present chapter, some knowledge of truths as
But first of all we
its source and ground.
"
must make clear what we mean by acquaint"
"
and what we mean by description."
ance
We shall say that w^e have acquaintance

with anything of which we are directly aware,
without the intermediary of any process of
inference or

any knowledge

of truths.

Thus

my table I am acquainted
with the sense-data that make up the appearance of my table its colour, shape, hardness,
in the presence of



smoothness,

etc.

;

all

these are things of

which am immediately conscious when I am
The particular
seeing and touching my table.
shade of colour that I am seeing may have
I



things said about it I may say that it
brown, that it is rather dark, and so on.

many
is

But such statements, though they make me
know truths about the colour, do not make me
know the colour itself any better than I did
before

colour

:

so far as concerns knowledge of the
itself, as opposed to knowledge of

I know the colour perfectly
I see it, and no further
when
and completely

truths about

knowledge of

it,

it

itself

is

even theoretically

THE PROBLEMS OF PHILOSOPHY

74

Thus the sense-data which make

possible.

up the appearance

of

my

table are things

with which I have acquaintance, things im-

known

mediately

to

me

just as they are.

My

knowledge of the table as a physical
object, on the contrary, is not direct know-

Such as

it is, it is obtained through
the sense-data that make
with
acquaintance
up the appearance of the table. We have

ledge.

seen that

it is

possible, without absurdity, to

doubt whether there is a table at all, whereas
it is not possible to doubt the sense-data.
My
knowledge of the table is of the kind which we
shall call

"

knowledge by description."

The

"

the physical object which causes
This describes
such-and-such sense-data."
table

is

the table by means of the sense-data. In
order to know anything at all about the
table,

we must know

truths connecting

it

with things with which we have acquaint"
such-and-such
we must know that
ance
:

sense-data are caused by a physical object."

There

is

no

state of

directly aware

mind

of the table

ledge of the table

is

in
;

really

which we are
all

our know-

knowledge

of

ACQUAINTANCE AND DESCRIPTION
and the actual thing which

truths,

table

at

is

all.

not, strictly speaking,

We know

that there

is

is

75
the

known to us
and we know

a description,
just one object to which this

description applies, though the object itself
In such a case,
is not directly known to us.

we say that our knowledge

of the object is

knowledge by description.
All our knowledge, both knowledge of,
things and knowledge of truths, rests upon
acquaintance as

its

foundation.

fore

to

consider what kinds of

important

things there are with which

It is there-

we have acquaint-

ance.

Sense-data, as

among

the

we have

already seen, are

things with which we are ac-

in fact, they supply the most
quainted
obvious and striking example of knowledge
;

by acquaintance. But if they were the sole
example, our knowledge would be very much
more restricted than it is. We should only
know what is now present to our senses we
:

could not

know anything about the past



—not

even that there was a past nor could we
know any truths about our sense-data, for all

THE PROBLEMS OF PHILOSOPHY

76

knowledge of truths, as we shall show, demands acquaintance with things which are of

an

from sensedata, the things which are sometimes called
"
abstract ideas," but which we shall call
"

essentially different character

universals."

We

have therefore to con-

i|ider acquaintance with other things besides
sense-data if we are to obtain any tolerably

adequate analysis of our knowledge.

The

extension beyond sense-data to
be considered is acquaintance by memory.
first

we

remember what
we have seen or heard or had otherwise
present to our senses, and that in such cases
we are still immediately aware of what we
It

is

obvious that

often

remember, in spite of the fact that it appears
as past and not as present.
This immediate
knowledge by memory is the source of all
our knowledge concerning the past
without
it, there could be no knowledge of the past by
:

inference, since

we should never know

that

there was anything past to be inferred.
The next extension to be considered

is

acquaintance by introspection. We are not
only aware of things, but we are often aware

ACQUAINTANCE AND DESCRIPTION
of being
I

"

aware of them.

am

often aware of

my

seeing the sun

When

77

I see the sun,

my

seeing the sun

''

an object with which

is

;

thus

have acquaintance. When I desire food, I
may be aware of my desire for food thus
I

;

*'

"

an object with which
I
Similarly we may be
aware of our feeling pleasure or pain, and
generally of the events which happen in our

my desiring food
am acquainted.

is

This kind of acquaintance, which
called
be
self-consciousness, is the source
may
It is
of all our knowledge of mental things.
minds.

obvious that

it is

only what goes on in our

own minds that can be thus known immediately. What goes on in the minds of others
is known to us through our perception of their
bodies, that is, through the sense-data in us
which are associated with their bodies. But
for our acquaintance with the contents of our

own minds, we

should be unable to imagine
the minds of others, and therefore we could

never arrive at the knowledge that they have
minds. It seems natural to suppose that
self-consciousness

distinguish

men

is

one of the things that

from animals

:

animals,

we

THE PROBLEMS OF PHILOSOPHY

78

suppose, though they have acquaintance
with sense-data, never become aware of this
acquaintance, and thus never know of their

may

own

existence.

I

do not mean that they

doubt whether they exist, but that they have
never become conscious of the fact that they

have sensations and feehngs, nor therefore

of

the fact that they, the subjects of their
sensations and feehngs, exist.

We have spoken of acquaintance with the
contents of our minds as seZ/-consciousness,
but
self

it is
:

it

not, of course, consciousness of our
is

consciousness

thoughts and feehngs.

we

of

particular

The question whether

are also acquainted with oui bare selves,

as opposed to particular thoughts and feelings,

a very difficult one, upon which it would
be rash to speak positively. When we try to
is

we always seem to come
some
upon
particular thought or feeling, and
" "
not upon the
I
which has the thought or
Nevertheless
there are some reasons
feeling.
look into ourselves

we are acquainted with the
the
though
acquaintance is hard to
disentangle from other things. To make clear
for thinking that

"

I,"

1

ACQUAINTANCE AND DESCRIPTION
what
a

sort of reason there

is,

79

let us consider for

moment what our acquaintance with

par-

ticular thoughts really involves.

When

am

*'

acquainted with
my seeing
the sun," it seems plain that I am
acquainted
with two different things in relation to each
other.
On the one hand there is the senseI

datum which represents the sun to me, on the
other hand there is that which sees this
sense-datum.

All acquaintance, such as

my

acquaintance with the sense-datum which
represents the sun, seems obviously a relation
between the person acquainted and the object
with which the person

is

acquainted.

When

a case of acquaintance

is one with which I
can be acquainted (as I am acquainted with
my acquaintance with the sense-datum re-

presenting the sun),

it is

plain that the person

acquainted
Thus, when I am
myself.
acquainted with my seeing the sun, the whole
"
fact with which I am
Selfacquainted is
is

acquainted-with-sense-datum."
Further,

we know the

truth

"

quainted with this sense-datum."
to see

how we could know

this

I

am

It

is

ac-

hard

truth,

or

THE

80

PROr.LE^lS OF PPIIL030PIIY

even understand what is meant by it, unless
we were acquainted with something which we
"
It docs not seem necessary to
I."
call
suppose that we are acquainted with a more

permanent person, the same to-day as
yesterday, but it does seem as though we
must be acquainted with that thing, whatever

or less

its

nature, which sees the sun and has ac-

quaintance with sense-data.
sense

it

Thus, in some

would seem we must be acquainted

with our Selves as opposed to our particular
experiences.

But the question

is

difficult,

and complicated arguments can be adduced
on either side. Hence, although acquaintance
with ourselves seems probably to occur, it is
not wise to assert that it undoubtedly does
occur.

We may

therefore

sum up

as follov/s

what

has been said concerning acquaintance with
things that exist. We have acquaintance in
sensation with the data of the outer senses,

and

may

in introspection with the data of

be

called

the inner sense

we have acquaintance
with things which have been data

feelings, desires, etc.

in

memory

what

— thoughts,

;

ACQUAINTANCE AND DESCRIPTION

81

either of the outer senses or of the inner sense.

Further,

it is

probable, though not certain, that
Self, as that which

we have acquaintance with
is

aware of things or has desires towards things.

In addition to our acquaintance with particular existing things, we also have acquaintance with what we shall

call universals,

that

to say, general ideas, such as whiteness,
diversity, brotherhood, and so on.
Every comis

plete sentence

must contain at

least

which stands for a universal, since
have a meaning which is universal.

one word
all

We

verbs
shall

return to universals later on, in Chapter IX ;
for the present, it is only necessary to guard
against the supposition that whatever

we can

be acquainted with must be something particular
is

and

existent.

called conceiving,

we

are aware

It will

is

Awareness of universals
and a universal of which

called a concept.

be seen that

the objects with
which we are acquainted are not included
physical objects (as opposed to sense-data),

among

nor other people's minds. These things are
known to us by what I call " knowledge by
description," which

we must now

consider.

THE PROBLEMS OF PHILOSOPHY

82

"

"
I mean any phrase of
description
"
"
the form
a so-and-so
or "the so-and-so."
"
A phrase of the form a so-and-so " I shall
"
"
call an
a phrase
ambiguous
description
"
"
of the form
the so-and-so
(in the singular)
"
"

By

a

;

I shall call

"

"

man "
the man
a

a

is

definite
Thus
description.
an ambiguous description, and

with the iron mask

"

is

a definite

There are various problems condescription.
nected with ambiguous descriptions, but I
pass them by, since they do not directly concern the matter we are discussing, which is the

nature of our knowledge concerning objects
in cases where we know that there is an object

answering to a definite description, though
we are not acquainted with any such object.
This is a matter which

is

concerned exclusively

with definite descriptions. I shall therefore, in
"
"
the sequel, speak simply of
descriptions
"
Thus

when

I

mean

a description
"
the

form

We

definite descriptions."

will

mean any phrase

so-and-so

"
so-and-so,"

of the

in the singular.

"

known by
when we know that it is " the
i.e. when we know that there is

shall say that

description

"

an object

is

ACQUAINTANCE AND DESCRIPTION

88

one object, and no more, having a certain
and it will generally be implied
property
;

we do not have knowledge of the same
We know that the
object by acquaintance.
man with the iron mask existed, and many
propositions are known about him but we do
not know who he was. We know that the
candidate who gets the most votes v/ill be
elected, and in this case we are very likely also
that

;

acquainted (in the only sense in which one
can be acquainted with some one else) with
the

man who

is,

in fact, the candidate

who will

get most votes but we do not know which of
the candidates he is, i.e. we do not know any
"
A is the candidate
proposition of the form
"
who will get most votes where A is one of
the candidates by name. We shall say that
we have " merely descriptive knowledge " of
;

the so-and-so when, although we know^ that
the so-and-so exists, and although we may
possibly be acquainted with the object which
is, in fact, the so-and-so, yet we do not know

any proposition
a

"

a

is

the so-and-so," where

something with which we are acquainted.
When we say " the so-and-so exists," we

is

THE PROBLEMS OF PHILOSOPHY

84

mean that

there

so-and-so.

so

"

is

just one object which

The proposition

"

a

is

means that a has the property

and nothing else has.

" Mr. A.

is

the

the so-andso-and-so,

the Unionist
"
candidate for this constituency
means
"
Mr. A. is a Unionist candidate for this
is

"The
constituency, and no one else is."
Unionist candidate for this constituency
"
some one is a Unionist candiexists" means
date for this constituency, and no one else is."
Thus, when we are acquainted with an object

which

the so-and-so,
so-and-so exists but we
is

;

we know that
may know that

the
the

when we are not acquainted
with any object which we know to be the soand-so, and even when we are not acquainted
so-and-so exists

with any object which, in fact, is the so-and-so.
Common words, even proper names, are
usually really descriptions. That is to say,
the thought in the mind of a person using a

name

correctly can generally only be
expressed explicitly if we replace the proper

proper

name by a

description.

Moreover, the de-

scription required to express the thought will

vary for different people, or for the same

ACQUAINTANCE AND DESCRIPTION

85

person at different times. The only thing
constant (so long as the name is rightly used)
is the object to which the name applies.
But
so long as this remains constant, the particular

description involved usually makes no difference to the truth or falsehood of the proposition in

which the name appears.

Let us take some

illustrations.

Suppose

some statement made about Bismarck.
suming that there

is

As-

such a thing as direct

acquaintance with oneself, Bismarck himself
might have used his name directly to designate the particular person with whom he was
acquainted. In this case, if he made a

judgment about himself, he himself might be
a constituent of the judgment. Here the
proper

name has the

direct use

which

it

always wishes to have, as simply standing for
a certain object, and not for a description
of the object.

But

if

a person

who knew

Bismarck made a judgment about him, the
case is different. What this person was acquainted with were certain sense-data which
he connected (rightly, we will suppose) with
Bismarck's body.

His body, as a physical

86

THE PROBLEMS OF PHILOSOPHY

more his mind, were only
known as the body and the mijid connected
with these sense-data. That is, they were
and

object,

still

known by description. It is, of course, very
much a matter of chance which characteristics of

friend's

a man's appearance will come into a
of him
thus

mind when he thinks

;

the description actually in the friend's mind
is accidental.
The essential point is that he

knows that the various descriptions all apply
same entity, in spite of not being ac-

to the

quainted with the entity in question.
When we, who did not know Bismarck,

make a judgment about him,
in our

minds

will

the description

probably be some more or



vague mass of historical knowledge far
more, in most cases, than is required to idenless

But, for the sake of illustration, let
"
us assume that we think of him as
the first

tify

him.

German Empire."

Here
all the words are abstract except
German."
The word " German" will, again, have different meanings for different people. To some it
will recall travels in Germany, to some the
look of Germany on the map, and so on. But
Chancellor of the

"

ACQUAINTANCE AND DESCRIPTION

87

we are to obtain a description which we
know to be applicable, we shall be compelled,
at some point, to bring in a reference to a
particular with which we are acquainted.
if

Such reference

involved in any mention of
and
future (as opposed to
past, present,
definite dates), or of here and there, or of what
others have told us. Thus it would seem that,
in some way or other, a description known to
is

be applicable to a particular must involve
some reference to a particular with which we
are acquainted,

thing described

if

our knowledge about the
to be merely what follows

is not

from the description. For example,
"the most long-lived of men" is a description
involving only universals, which must apply to
logically

some man, but we can make no judgments concerning this man which involve knowledge
about him beyond what the description
gives.
"
The first Chancellor of
If, however, we say,
the German Empire was an astute
diplomatist,"
of our

we can only be assured

judgment

in virtue of

of the truth

something with
which we are acquainted usually a
testimony
heard or read. Apart from the information



\

THE PROBLEMS OF PHILOSOPHY

88

we convey to others, apart from the

fact about

the actual Bismarck, which gives importance
to our judgment, the thought we really have
contains the one or more particulars involved,
and otherwise consists wholly of concepts.
All

names



of

places London, England,
the Solar System simi,the
Earth,
Europe,
larly involve,

start



when

from some

used, descriptions which
one or more particulars with

which we are acquainted.

I suspect that

even

the Universe, as considered by metaphysics,
involves such a connection with particulars.

In

logic,

on the contrary, where we are

concerned not merely with what does exist,
but with whatever might or could exist or
be,

no reference to actual

particulars

is

involved.

would seem that, when we make a
statement about something only known by
It

description,

we

often intend to

make our

statement, not in the form involving the
description, but about the actual thing de-

That is to say, when we say anything about Bismarck, we should like, if we
could, to make the judgment which Bismarck
scribed.

ACQUAINTANCE AND DESCRIPTION

89

alone can make, namely, the judgment of
which he himself is a constituent. In this

we

are necessarily defeated, since the actual
But we know
is unknown to us.

Bismarck

that there

B

and that

an object B, called Bismarck,
was an astute diplomatist. We

is

can thus describe the proposition we should
"
namely, B was an astute diplo-

like to affirm,

matist," where

Bismarck.
" the

first

B

is

the object which was

If we are describing Bismarck as
Chancellor of the German Empire,"

the proposition we should like to affirm may
"
the proposition asserting,
be described as
concerning the actual object which was the
first

Chancellor of the

this

What

German Empire,

that

object was an astute diplomatist."
enables us to communicate in spite of

the varying descriptions we employ is that
we know there is a true proposition concerning
the actual Bismarck, and that however

may

we

vary the description (so long as the

description is correct) the proposition described is still the same. This proposition,

which
is

is

described and

is

known

to be true,

what interests us but we are not acquainted
;

90

THE PROBLEMS OF PHILOSOPHY

with the proposition

itself,

and do not know

though we know it is true.
It will be seen that there are various stages
in the removal from acquaintance with
it,

particulars

:

there

is

Bismarck to people who

knew him, Bismarck to those who only know
of him through history, the man with the
These
iron mask, the longest -lived of men.
are progressively further removed from acquaintance with particulars the first comes
;

as near to acquaintance as

is

possible

in

regard to another person ; in the second, we
shall still be said to know "who Bismarck
"
was ; in the third, we do not know who

was the man with the iron mask, though we
many propositions about him which
are not logically deducible from the fact that

can know

he wore an iron mask

;

in the fourth, finally,

we know nothing beyond what

is

logically

deducible from the definition of the man.

There

is

a similar hierarchy in the region of

Many universals, like many parare
ticulars,
only known to us by description.
But here, as in the case of particulars, knowuniversals.

ledge concerning what

is

known by

descrip-

ACiJUAINTANCE AND DESCRIPTION
tion

ultimately reducible

is

to

91

knowledge

concerning what is known by acquaintance.
The fundamental principle in the analysis
of propositions containing descriptions

is

this

:

Every 'proposition which we can understand]
must be composed wholly of constituents with
ivhich

we are acquainted.

We
answer

not at this stage attempt to
the objections which may be urged

shall
all

against this fundamental principle.
present,

we

shall

For the

merely point out that, in

some way or other, it must be possible to
meet these objections, for it is scarcely
conceivable that we can make a judgment
or entertain a supposition without knowing
what it is tliat we are judging or supposing

We

must attach some meaning to
the words we use, if we are to speak signiand the
ficantly and not utter mere noise
meaning we attach to our words must be
something with which we are acquainted.
Thus when, for example, we make a statement about Julius Ctesar, it is plain that
about.

;

not before our minds,
We
since we are not acquainted with him.

Julius Csesar himself

is

92

THE PROBLEMS OF PHILOSOPHY

have

in

Caesar

:

mind some
"

the

description

man who was

Julius

of

assassinated on

the Ides of March," "the founder of the Roperhaps, merely "the man
was Julius CcBsar." (In this last

man Empire,"
whose name

or,

a noise or shape
Thus our
are acquainted.)

description, Julius Cossar

with which we

statement does not
to

mean,

mean

is

quite

what

it

seems

but means something involving,

instead of Julius Caesar, some description of

him which is composed wholly of particulars
and universals with which we are acquainted.
The chief importance of knowledge by
description is that it enables us to pass
beyond the limits of our private experience.
In spite of the fact that we can only know

truths which are wholly composed of terms

which we have experienced in acquaintance,
we can yet have knowledge by description
which we have never experienced.
In view of the very narrow range of our
immediate experience, this result is vital,
of things

and

until

it is

understood,

much

of our

know-

ledge must remain mysterious and therefore
doubtful.

CHAPTER VI
ON INDUCTION
In almost

our previous discussions we
have been concerned in the attempt to get
all

clear as to our data in the
of existence.

way

of

knowledge

What

things are there in the
universe whose existence is known to us owing
to our being acquainted with

our answer has been that

them

?

So

far,

we

are acquainted
with our sense-data, and, probably, with ourselves.

These we know to

sense-data which are

And past
remembered are known

to have existed in the

exist.

past.

ledge supplies our data.
But if we are to be able to

from these data



if

we

This know-

draw

are to

inferences

know

of the

existence of matter, of other people, of the
past before our individual memory begins,
or of tiie future, we must know general
prin93

THE PROBLEMS OF PHILOSOPHY

94

some kind by means of which such
It must be known
of
some one sort of
to us that the existence
of
is
a
the
existence
of some
A,
sign
thing,
of
either
at
the
sort
same
other
time
thing, B,
as A or at some earher or later time, as, for
ciples of

inferences can be drawn.

a sign of the earlier
If this were not known
existence of lightning.
to us, we could never extend our knowledge
example, thunder

is

beyond the sphere of our private experience
and this sphere, as we have seen, is exceedingly limited. The question we have now to
consider is whether such an extension is
;

possible,

and

if

so,

how

it is

effected.

Let us take as an illustration a matter about

which none of

us, in fact, feel the slightest

doubt.

We

will rise

to-morrow.

are

all

mere blind outcome
can
is

convinced that the sun

Why

?

Is this belief

a

of past experience, or

be justified as a reasonable belief ? It
not easy to find a test by which to judge
it

whether a
not, but

belief of this

we can

is

reasonable or

at least ascertain

would

what

sort

if

true, to

judgment that the sun

will rise

of general beliefs
justify the

kind

suffice,

ON INDUCTION

95

to-morrow, and the many other similar judgments upon which our actions are based.
It is obvious that

if

we

are asked

why we
we

believe that the sun will rise to-morrow,
shall

"

Because it always
has risen every day." We have a firm belief
that it will rise in the future, because it has
risen in the past.
If we are challenged as to
naturally answer,

why we

believe that

as heretofore,

motion

:

the

it will

continue to

rise

we may appeal to the laws of
earth, we shall say, is a freely

rotating body, and such bodies do not cease
to rotate unless something interferes from
outside,

and there

is

nothing

interfere with the earth

to-morrow.

Of course

it

outside

to

between now and
might be doubted

whether we are quite certain that there is
nothing outside to interfere, but this is not
the

doubt.
The interesting
interesting
doubt is as to whether the laws of motion

remain in operation until to-morrow. If
this doubt is raised, we find ourselves in the
will

same position as when the doubt about the
sunrise was first raised.

The only reason

for believing that the laws

96

THE PROBLEMS OF PHILOSOPHY

motion will remain in operation is that
they have operated hitherto, so far as our
knowledge of the past enables us to judge.
It is true that we have a greater body of
evidence from the past in favour of the laws
of motion than we have in favour of the sunof

because the sunrise

merely a particular
case of fulfilment of the laws of motion, and
rise,

is

there are countless other particular cases.
But the real question is
Do any number
:

of cases of a law being fulfilled in the past
afford evidence that it will be fulfilled in the
?
If not, it becomes plain that we
have no ground whatever for expecting the
sun to rise to-morrow, or for expecting the
bread we shall eat at our next meal not to

future

poison us, or for any of the other scarcely
conscious expectations that control our daily
lives.

It

is

to be observed that

all

such

expectations are only probable thus we have
not to seek for a proof that they must be ful;

but only for some reason in favour of
the view that they are likely to be fulfilled.
filled,

Now in dealing with this question we must,
to begin with, make an important distinction,

ON INDUCTION

97

without which we should soon become involved in hopeless confusions. Experience
has shown us that, hitherto, the
frequent
repetition

of

some uniform succession or

coexistence has been a cause of our
expecting
the same succession or coexistence on the

next

occasion.

Food that has a

certain

appearance generally has a certain taste, and
it is a severe shock to our
expectations when
the familiar appearance is found to be associated with an unusual taste.

Things which
associated, by habit, with
certain tactile sensations which we
expect
if we touch them
one of the horrors of a

we

become

see

;

ghost (in many ghost-stories) is that it fails
to give us any sensations of touch.
Uneducated people who go abroad for the first time
are so surprised as to be incredulous when

they find their native language not understood.

to

A

And this kind of association is not confined
men in animals also it is very strong.
;

horse which has been often driven
along a
certain road resists the
attempt to drive him
in

a different direction.

D

Domestic animals

THE PROBLEMS OF PHILOSOPHY

98

expect food when they see the person who
usually feeds them. We know that all these
rather crude expectations of uniformity are
liable to be misleading.
The man who has

fed the chicken every day throughout its life
at last wrings its neck instead, showing that

more

refined views as to the uniformity of

nature would have been useful to the chicken.

But

in spite of the misleadingness of such

expectations, they nevertheless exist. The
mere fact that something has happened a
certain

men

number

of times causes animals

to expect that

Thus our instincts

it

and

will

happen again.
certainly cause us to believe

that the sun will rise to-morrow, but

we may

be in no better a position than the chicken
which unexpectedly has its neck wrung. We
have therefore to distinguish the fact that
past uniformities cause expectations as to the
future, from the question whether there is
for giving weight to
such expectations after the question of their
validity has been raised.

any reasonable ground

The problem we have to discuss
there is any reason for believing

is

in

whether

what

is

ON INDUCTION
called

"

the

of

uniformity

belief in the uniformity of

99

nature."

nature

is

The

the belief

that everything that has happened or will
happen is an instance of some general law
to which there are no exceptions. The crude

expectations which we have been considering
are all subject to exceptions, and therefore
liable to disappoint those

who entertain them.

But science habitually assumes, at

least as

a

working hypothesis, that general rules
which have exceptions can be replaced by

which have no exceptions.
"
bodies
in air fall
is a general
Unsupported
rule to which balloons and aeroplanes are
general
"

rules

But the laws of motion and the
exceptions.
law of gravitation, which account for the
fact that

most bodies

fall,

also account for

the fact that balloons and aeroplanes can rise ;
thus the laws of motion and the law of gravitation are not subject to these
exceptions.

The

belief that the sun will rise to-morrow
be
falsified if the earth came
might
suddenly
into contact with a large body which
destroyed
its rotation
but the laws of motion and the
law of gravitation would not be
;

infringed

by

100

THE PROBLEMS OF PHILOSOPHY

such an event.

The business

of science

find uniformities, such as the laws of

is

to

motion

and the law

of gravitation, to which, so far
as our experience extends, there are no exIn this search science has been
ceptions.

remarkably successful, and it may be conceded
that such uniformities have held hitherto.

Have
This brings us back to the question
we any reason, assuming that they have
:

always held in the past, to suppose that they
will hold in the future ?
It has

been argued that we have reason to

know

that the future will resemble the past,
because what was the future has constantly

become the

past,

and has always been found

to resemble the past, so that we really have
experience of the future, namely of times

which were formerly future, which we may
But such an argument
call past futures.
really begs the very question at issue.

We

have experience of past futures, but not of
future futures, and the question is Will future
:

futures resemble past futures ? This question is not to be answered by an argument

which starts from past futures alone.

We

ON INDUCTION
have therefore

still

to seek for

which shall enable us to
will follow

The

know

some

101
principle

that the future

the same laws as the past.

reference to the future in this question

not essential. The same question arises
when we apply the laws that work in our
experience to past things of which we have

is

no experience



as,

for example, in geology,

or in theories as to the origin of the Solar
System. The question we really have to ask
"
is
When two things have been found to be
often associated, and no instance is known
:

of the one occurring without the other, does

the occurrence of one of the two, in a fresh
instance, give

the other

?

"

any good ground for expecting
On our answer to this question

must depend the

validity of the whole of our

expectations as to the future, the whole of
the results obtained by induction, and in fact
practically all

daily

life is

the beliefs upon which our

based.

It must be conceded, to begin with, that
the fact that two things have been found often
together and never apart does not, by itself,
suffice

to prove demonstratively that they

THE PROBLEMS OF PHILOSOPHY

102

be found together in the next case we
examine. The most we can hope is that the
will

oftener things are found together, the more
probable it becomes that they will be found

together another time, and that, if they have
been found together often enough, the probIt
ability will amount almost to certainty.

can never quite reach certainty, because we

know

that in spite of frequent repetitions
is a failure at the last, as

there sometimes

in the case of the chicken

whose neck is wrung.

Thus probability

we ought

is all

to seek.

It might be urged, as against the view we
are advocating, that we know all natural
phenomena to be subject to the reign of law,

and that sometimes, on the

basis of observa-

we can see that only one law can possibly
the facts of the case. Now to this view

tion,
fit

there are two answers.

The

first

is

that,

some law which has no exceptions
to
our case, we can never, in practice,
applies
be sure that we have discovered that law and
even

if

not one to which there are exceptions. The
second is that the reign of law would seem to

be

itself

only probable, and that our belief

ON INDUCTION
that

it

will

hold in the future, or in unexamined

cases in the past,

is itself

based upon the very

we

are examining.
principle we are examining

principle

The

103

called the principle of induction,

parts
(a)

be stated as follows

may
When

may

and

be

its

two

A

has

:

a thing of a certain sort

been found to be associated with a thing of a
certain other sort B, and has never been found
dissociated from a thing of the sort B, the
greater the number of cases in which A and B

have been associated,

greater is the
probability that they will be associated in a
fresh case in which one of them is known to

be present
(6)

cient

the

;

Under the same circumstances, a suffinumber of cases of association will make

the probability of a fresh association nearly

a certainty, and will make
tainty without limit.

it

approach

cer-

As

just stated, the principle applies only to
the verification of our expectation in a single

fresh instance.

that there

is

But we want

also to

know

a probability in favour of the
A are

general law that things of the sort

THE PROBLEMS OF PHILOSOPHY

104

always associated with things of the sort B,
provided a sufficient number of cases of

known, and no cases of failure
of association are known.
The probabihty of
the general law is obviously less than the
association are

probability of the particular case, since if
the general law is true, the particular case
must also be true, whereas the particular

case

may be true without the general law being
Nevertheless the

true.

general law

is

the

of

probability

increased

by repetitions, just
as the probability of the particular case is.
may therefore repeat the two parts of

We

our principle as regards the
thus

general

law,

:

(a)

The greater the number

which a thing of the sort

A

of

cases

in

has been found

associated with a thing of the sort B, the more
probable it is (if no cases of failure of association are

with
{b)

cient

B

known) that

A

is

always associated

;

Under the same circumstances, a suffinumber of cases of the association of

A

with

is

always associated with B,

B

will

make

it

nearlv certain that

and

will

A

make

ON INDUCTION

105

law approach certainty without

this general
limit.

should

It

be noted that probability is
In our case,

always relative to certain data.

the data are merely the known cases of coexistence of A and B. There may be other

which might be taken into account,
which would gravely alter the probability.
For example, a man who had seen a great
many white swans might argue, by our principle, that on the data it was probable that all
data,

swans were white, and this might be a perThe argument is
fectly sound argument.
not disproved by the fact that some swans
are black, because a thing may very well
happen in spite of the fact that some data

render

it

swans, a

improbable.

In the case of the

man might know

that colour

very variable characteristic in
of animals,

as

and

this

a

species

that, therefore, an induction

peculiarly liable to error.
knowledge would be a fresh datum,

to colour

But

many

is

is

by no means proving that the probability
relatively to our previous data had been
wrongly estimated. The fact, therefore, that

106

THE PROBLEMS OF PHILOSOPHY

things often fail to fulfil our expectations
is no evidence that our expectations will not

probably be fulfilled in a given case or a given
Thus our inductive principle

class of cases.

any rate not capable of being disproved
by an appeal to experience.
The inductive principle, however, is equally
incapable of being proved by an appeal to
is

at

Experience might conceivably
experience.
confirm the inductive principle as regards the
cases that have been already examined ; but
as regards unexamined cases, it is the in-

ductive principle alone that can justify any
inference from what has been examined to

what has not been examined.

All arguments

which, on the basis of experience, argue as
to the future or the unexperienced parts of the
past or present, assume the inductive principle ; hence we can never use experience to

prove the inductive principle without begging
the question. Thus we must either accept
the inductive principle on the ground of its
intrinsic evidence, or forgo all justification
1

of our expectations

principle

is

about the future.

If

the

unsound, we have no reason to

ON INDUCTION

107

expect the sun to rise to-morrow, to expect
bread to be more nourishing than a stone, or
to expect that if we throw ourselves off the
roof

we

shall fall.

When we

see

what looks

our best friend approaching us, we shall
have no reason to suppose that his body is
not inhabited by the mind of our worst enemy

like

or of

some

total stranger.

All our conduct

is

based upon associations which have worked
in the past, and which we therefore regard as

work

likely to

hood

is

and

this likeli-

for its validity

upon the

in the future

dependent

;

inductive principle.
principles of science, such as
the belief in the reign of law, and the belief

The general

that every event must have a cause, are as
completely dependent upon the inductive
All
principle as are the beliefs of daily life.
because
believed
are
such general principles

mankind have found innumerable instances of
their truth, and no instances of their falsehood. But this affords no evidence for their
truth in
principle

Thus

the future,
is

all

unless

the

inductive

assumed.

knowledge which, on a basis of

THE PROBLEMS OF PHILOSOPHY

108

experience, tells us something about what is
not experienced, is based upon a belief which
experience can neither confirm nor confute,

yet which, at least in its more concrete applications, appears to be as firmly rooted in us

the facts of experience. The
existence and justification of such beliefs
as

many

of



for the inductive principle, as
is

not the

most


only example

difficult

we

shall see,

raises some of the
and most debated problems of

philosophy. We will, in the next chapter,
consider briefly what may be said to account
for

such knowledge, and what

its

degree of certainty.

is its

scope and

CHAPTER

VII

ON OUR KNOWLEDGE OF GENERAL PRINCIPLES

We

saw

in

experience,

is

the preceding chapter that
the principle of induction, while necessary
to the validity of all arguments based on

not capable of being

itself

proved by experience, and yet is unhesitatingly believed by every one, at least in all its
concrete

applications.

In

these

character-

the principle of induction does not stand
alone.
There are a number of other prin-

istics

which cannot be proved or disproved by
experience, but are used in arguments which
ciples

start

from what

Some

is

experienced.

of these principles

evidence than

the

and the knowledge

have even greater

principle
of

of

induction,

them has the same

degree of certainty as the knowledge of the
existence of sense-data.
They constitute the
109

THE PROBLEMS OF PHILOSOPHY

110

drawing inferences from what is
and if what we infer is
given in sensation
to be true, it is just as necessary that our

means

of

;

principles of inference should be true as
is

The

that our data should be true.

it

prin-

ciples of inference are apt to be overlooked
because of their very obviousness the as-



assented to without our

sumption involved

is

realising that

an assumption.

it is

But

it is

very important to realise the use of principles
of inference, if a correct theory of knowledge
is

to be obtained

;

raises interesting

for our

and

knowledge

difficult

of

them

questions.

our knowledge of general principles,
what actually happens is that first of all we
In

all

some particular application
principle, and then we realise that the
realise

larity

is

irrelevant, andthatthere

is

of

the

particu-

a generality

equally truly be affirmed. This
is of course familiar in such matters as teach"
"
two and two are four is
ing arithmetic

which

may

:

first

case,

some particular pair
some other particular
at last it becomes possible

learnt in the case of

of couples,

and

and then

so on, until

to see that

it is

in

true of any pair of couples.

GENERAL PRINCIPLES

111

The same thing happens with logical prinSuppose two men are discussing
ciples.
what day of the month it is. One of them
"
At least you will admit that if yestersays,
day was the 15th to-day must be the 16th."
"Yes," says the other, "I admit that."
"
And you know," the first continues, "that
yesterday was the 15th, because you dined
with Jones, and your diary will tell you that
"
was on the 15th."
Yes," says the second
;

"

therefore to-day is

the 16th."

Now such an argument is not hard to follow
and

if it is

in fact,

must

granted that

no one

also be

will

true.

;

premisses are true
that the conclusion

its

deny
But

depends for

it

its

truth upon an instance of a general logical
The logical principle is as follows
principle.
"
Suppose it known that if this is true, then
:

that

is

true.

is true,

When
is

true,

Suppose

then

it is

we

it

it

also

known

follows that that

the case that

if

that this
is

true."

this is true, that

shall say that this

"

"
implies

"
and that that " follows from

this.

that,

Thus

our principle states that if this implies that,
and this is true, then that is true. In other

THE PROBLEMS OF PHILOSOPHY

112

"

anything implied by a true pro"
whatever follows from
position is true," or
words,

a true proposition is true."
This principle is really involved

least,

concrete instances of

in all

demonstrations.

we

believe

is

it

are

—at
involved—

Whenever one thing which

used to prove something

which we consequently
If
is
relevant.
any

else,

believe, this principle

one

asks

"
:

Why

accept the results of valid arguments
"
we can only
based on true premisses ?
answer by appealing to our principle. In

should

I

the truth of the principle is impossible
and its obviousness is so great that
Such
at first sight it seems almost trivial.
fact,

to doubt,

principles,

however, » are not

trivial

to the

show that we may have
indubitable knowledge which is in no way
derived from objects of sense.
The above principle is merely one of a
certain number of self-evident logical prinSome at least of these principles must
ciples.
philosopher, for they

be granted before any argument or proof
becomes possible. When some of them have

been granted, others can be proved, though

GENERAL PRINCIPLES

113

these others, so long as they are simple, are
for
just as obvious as the principles taken
of
granted. For no very good reason, three
out
been
have
these principles
by
singled
"
Laws of
tradition under the name of

Thought."

They
(1)

are as follows

The

:

law of identity:

"Whatever

is,

is."

The law of contradiction :
can both be and not be."
(3) The law of excluded middle
thing must either be or not be."

"

(2)

Nothing
"

:

Every-

These three laws are samples of self-evident
more
logical principles, but are not really

fundamental or more self-evident than various
other similar principles for instance, the one
:

we

considered just now, which states that

what follows from a true premiss is true.
"
"
is also mislaws of thought
The name
is important is not the fact
for
what
leading,
that we think in accordance with these laws,
but the fact that things behave in accordance
with them in other words, the fact that when
we think in accordance with them we think
;

114

THE PROBLEMS OF PHILOSOPHY

But this is a
we must return at a

truly.

large question, to which
later stage.

In addition to the logical principles which
enable us to prove from a given premiss that
something is certainly true, there are other
logical principles

which enable us to prove,

from a given premiss, that there

is

or less probability that something

An example

of

such principles

example —

a greater
is

true.

—perhaps

the

is the inductive
most important
we
in the prewhich
considered
principle,

ceding chapter.
One of the great historic controversies in

philosophy is the controversy between the
two schools called respectively "empiricists "
"
rationalists."
The empiricists who
and



by the British philosophers, Locke, Berkeley, and Hume maintained that all our knowledge is derived from
are best represented





the rationalists who are repreexperience
sented by the Continental philosophers of the
;

seventeenth century, especially Descartes and
Leibniz maintained that, in addition to



what we know by experience, there are certain
"
**
"
and
innate principles,"
innate ideas

GENERAL PRINCIPLES

115

which we know independently of experience.
It has

now become

possible to decide with

some confidence as to the truth or falsehood

of

these opposing schools. It must be admitted,
for the reasons already stated, that logical
principles are

known

to us,

and cannot be

themselves proved by experience, since all
proof presupposes them. In this, therefore,

which was the most important point of the
controversy, the rationalists were in the
right.

On

the other hand, even that part of our

knowledge which

is logically

independent of

experience (in the sense that experience cannot prove it) is yet elicited and caused by
experience. It is on occasion of particular experiences that we become aware of the general
laws which their connections exemplify.
It would certainly be absurd to suppose that

there are innate principles in the sense that
babies are born with a knowledge of every-

thing which

men know and which

deduced from what
reason, the word

"

cannot be

experienced. For this
"
innate
would not now

is

be employed to describe our knowledge of

THE PROBLEMS OF PHILOSOPHY

116

The phrase " a pn'on " is
less objectionable, and is more usual in modern
writers. Thus, while admitting that all knowledge is elicited and caused by experience, we
shall nevertheless hold that some knowledge
logical principles.

is

priori^ in the sense that the experience

a

which makes us think

of it does not suffice to

prove it, but merely so directs our attention
that we see its truth without requiring any
proof from experience.

another point of great importance,
in which the empiricists were in the right

There

is

as against the rationalists.
Nothing can be
known to exist except by the help of experi-

we wish to prove
that something of which we have no direct
experience exists, we must have among our
ence.

That

is

to say,

if

premisses the existence of one or more things
of which we have direct experience. Our be-

Emperor of Russia exists, for
example, rests upon testimony, and testimony
lief

that the

consists,

in the last analysis, of sense-data

seen or heard in reading or being spoken
Rationalists believed that, from general
consideration as to what must be, they could
to.

GENERAL PRINCIPLES

117

deduce the existence of this or that in the
In this belief they seem to
actual world.
have been mistaken. All the knowledge that

we can

acquire a priori concerning existence
seems to be hypothetical it tells us that if
:

one thing

exists,

generally,

that

another must
if

exist, or,

more

one proposition is true,
This is exemplified by

another must be true.
the principles

we have already dealt with, such

as'' if this

true,

that

is

true," or

is

"

and

this implies that, then

if this

and that have been

repeatedly found connected, they will probably be connected in the next instance in

which one of them

and power

is

found."

Thus the scope

of a priori principles is strictly

knowledge that something exists
must be in part dependent on experience.

limited.

When

All

is known immediately, its
known by experience alone when

anything

existence

anything

is
is

;

proved to exist, without being

known immediately, both

experience and a
priori principles must be required in the proof.

Knowledge

is

called empirical

when

wholly or partly upon experience.

it

rests

Thus

all

knowledge which asserts existence is empirical.

118

THE PROBLEMS OF PHILOSOPHY

and the only a

among

knowledge concerning

priori

hypothetical, giving connections
things that exist or may exist, but

existence

is

not giving actual existence.
A priori knowledge is not

kind

we have been

all of

hitherto

the logical
considering.

Perhaps the most important example of nonis knowledge as to
logical a priori knowledge
ethical value.

I

ments as to what
virtuous,

for

am
is

such

not speaking of judguseful or as to

judgments

do

what

is

require

empirical premisses ; I am speaking of judgments as to the intrinsic desirability of things.

must be useful because
it secures some end; the end must, if we have
gone far enough, be valuable on its own account, and not merely because it is useful for
some further end. Thus all judgments as
to what is useful depend upon judgments as
to what has value on its own account.
If

something is useful,

We
more

it

judge, for example, that happiness is
desirable than misery, knowledge than

ignorance, goodwill than hatred, and so on.
Such judgments must, in part at least, be

immediate and a

priori.

Like our previous

GENERAL PRINCIPLES

119

a priori judgments, they may be elicited by
for it
experience, and indeed they must be
;

seems not possible to judge whether anything
is
intrinsically valuable unless we have

something of the same kind.
obvious that they cannot be

experienced

But

it is fairly

for the fact that a
proved by experience
thing exists or does not exist cannot prove
;

either that

that

it

is

it is

bad.

it

should exist or

The pursuit

of this subject

good that

ethics, where the impossibility
belongs
of deducing what ought to be from what is
has to be established. In the present con-

to

nection,

it is

only important to realise that
what is intrinsically of value

knowledge as to
is

a priori in the same sense in which logic

a priori, namely in the sense that the truth
of such knowledge can be neither proved nor

is

disproved by experience.

mathematics

a priori, like logic.
This was strenuously denied by the empirical
philosophers, who maintained that experience
All pure

was as much the source

is

of our

knowledge of

arithmetic as of our knowledge of geography.
They maintained that by the repeated ex-

120

THE PROBLEMS OF PHILOSOPHY

perience of seeing

two things and two other

things, and finding that altogether they made
four things, we were led by induction to the
conclusion that two things and two other

things would always
gether.

If,

make

four things altohowever, this were the source of

our knowledge that two and two are four,
we should proceed differently, in persuading
ourselves of its truth, from the way in which

we do actually proceed. In fact, a certain
number of instances are needed to make us
think of two abstractly, rather than of two
coins or two books or two people, or two of
any other specified kind. But as soon as we
are able to divest our thoughts of irrelevant
particularity, we become able to see the

general principle that two and two are four
any one instance is seen to be typical, and the
;

examination of other instances becomes unnecessary.*

The same thing is exemplified in geometry.
If we want to prove some property of all
triangles, we draw some one triangle and
*

Cf. A.

(Home

N. Whitehead, Introduction

University Library).

to

Mathematics

GENERAL PRINCIPLES

121

but we can avoid making
use of any property which it does not share
with all other triangles, and thus, from our

reason about

it

;

We
two

we obtain a

general result.
do not, in fact, feel our certainty that
and two are four increased by fresh

particular case,

instances, because, as soon as

we have seen

the truth of this proposition, our certainty
becomes so great as to be incapable of growing

some quality of
"
two and
necessity about the proposition
two are four," which is absent from even the
best attested empirical generalisations. Such
mere facts
generalisations always remain
in which
be
a
world
there
that
we feel
might
greater.

we

IVIoreover,

feel

:

they were

false,

though

in the actual

to be true.

world

In any possible

they happen
world, on the contrary, we feel that two and
two would be four this is not a mere fact,
:

but a necessity to which everything actual
and possible must conform.

The case may be made

clearer

by con-

sidering a genuinely empirical generalisation,
"
such as All men are mortal." It is plain that

we

believe this proposition, in the

first

place,

122

THE PROBLEMS OF PHILOSOPHY

no known instance of men
living beyond a certain age, and in the second
place because there seem to be physiological
grounds for thinking that an organism such
as a man's body must sooner or later wear

because there

out.

is

Neglecting

the

second

ground,

and

considering merely our experience of men's
mortality, it is plain that we should not be

content with one quite clearly understood!
instance of a man dying, whereas, in the case:
"
two and two are four," one instance doeji
of
suffice,

when

carefully considered, to persuade

us that the same must happen in any other
instance. Also we can be forced to admit,,

on reflection, that there may be some doubt,
however slight, as to whether all men are;
mortal.

This

may

be made plain by

the;

attempt to imagine two different worlds, in
one of which there are men who are not
mortal, while in the other two and two make
When Swift invites us to consider the
five.
race of Struldbugs who never die, we are
But a world
able to acquiesce in imagination.

where two and two make
a different

level.

five

seems quite on

We feel that such a world,

if

GENERAL PRINCIPLES

123

there were one, would upset the whole fabric
of our knowledge and reduce us to utter doubt.

The

fact

is

that, in simple mathematical

and

also in

"

two and two are four,"
many judgments of logic, we can

judgments such as

know the general
it

proposition without inferring
from instances, although some instance is

usually necessary to

make

clear to us

general proposition means.
is

This

is

what the

why there

real utility in the process of deduction,

which

goes from the general to the general or from
the general to the particular, as well as in the
process of induction, which goes from the particular to the particular, or from the particular
to the general. It is an old debate among

philosophers whether deduction ever gives
new knowledge. We can now see that in

we
make
two
and
two
that
know
always
already
four, and we know that Brown and Jones are
two, and so are Robinson and Smith, we can
deduce that Brown and Jones and Robinson
and Smith are four. This is new knowledge,

certain cases, at least,

it

does do

so.

If

not contained in our premisses, because the
"
are
general proposition,

two and two

four,"

\
"

'

f

124

THE PROBLEMS OF PHILOSOPHY

never told us there were such people as Brown
and Jones and Robinson and Smith, and the
there
particular premisses did not tell us that

were four of them, whereas the particular
proposition deduced does tell us both these
things.

But the newness of the knowledge is much
less certain if we take the stock instance of
deduction that
"

namely,
a man, therefore

logic,
is

always given in books on
All men are mortal Socrates

is

;

Socrates

is

mortal."

know beyond

In this case, what we really
reasonable doubt is that certain men, A,
B, C, were mortal, since, in fact, they have
died.

If Socrates is

one of these men,

it is

foiolish to go the roundabout way through
"
*'
to arrive at the conall men are mortal

mortal.

If

men on whom

our

clusion that probably Socrates

Socrates

is

induction

not one of the

is

based,

we

shall

is

still

do better to

argue straight from our A, B, C, to Socrates,
than to go round by the general proposition,
"
are mortal." For the
all

men

that Socrates

probability

is

mortal

is

greater, on our data,

than the probability that

all

men

are mortal.

GENERAL PRINCIPLES
obvious, because

(This

is

so

Socrates

is

;

but

does not follow that

Hence we

shall

if all

men are mortal,

Socrates

if

all

125

men

is

mortal,

it

are mortal.)

reach the conclusion that

mortal with a greater approach to
we make our argument purely
certainty
"
inductive than if we go by way of
all men
"
are mortal
and then use deduction.
Socrates

is

if

This

illustrates

the

general propositions
"
two and two are

difference

known a
four,"
"

priori,

between
such as

and empirical

all men are mortal."
generalisations such as
In regard to the former, deduction is the

mode

right

of argument,

the latter, induction

is

whereas in regard to
always theoretically

and warrants a greater confidence

preferable,

in the truth of our conclusion, because all

empirical generalisations are
than the instances of them.

more uncertain

We
tions

have now seen that there are proposiknown a priori, and that among them are

the propositions of logic and pure mathematics,
as well as the fundamental propositions of
ethics.

us

is

The question which must next occupy
this

:

How

is

it

possible that there

'

126

THE PROBLEMS OF PHILOSOPHY

should be such knowledge ? And more particularly, how can there be knowledge of
general propositions in cases where we have
not examined all the instances, and indeed

never can examine them

number
were
the

all,

These questions, which
brought prominently forward by

is infinite ?

first

German philosopher Kant

are very difficult,
portant.

because their

and

(1724-1804),

historically very im-

CHAPTER
HOW

KNOWLEDGE

A PRIORI

Immanuel Kant
the

VIII

of

IS

POSSIBLE

generally regarded as

is

modern

the

philosophers.
greatest
lived through the Seven Years'

Though he

War and

the French Revolution, he never

interrupted

Konigsberg

his

teaching

tinctive contribution

he called the

of

East Prussia.

in

"

philosophy at
His most dis-

was the invention of what

assuming as a datum

"

philosophy, which,
that there is knowledge

critical

of various kinds, inquired

how such know-

ledge comes to be possible, and deduced, from
the answer to this inquiry, many metaphysical results as to the nature of the world.

Whether these results were valid may well be
doubted. But Kant undoubtedly deserves
credit for two things
first, for having perceived that we have a priori knowledge wluch
:

127

THE PROBLEMS OF PHILOSOPHY

128

not

is

the

"

purely

analytic,"

would

opposite

and secondly,

for

be

i.e.

such that

self -contradictory

having made

;

evident the

importance of the theory of

philosophical

knowledge.
Before the time of Kant, it was generally
held that whatever knowledge was a priori

must be "

analytic.''

What

this

word means

be best illustrated by examples. If I
A bald man is a man," " A plane figure
say,
"
is a figure,"
A bad poet is a poet," I make
will

"

a purely analytic judgment
the subject
is
about
spoken
given as having at least two
:

properties, of which one is singled out to be
Such propositions as the above
asserted of it.
are trivial, and would never be enunciated in

except by an orator preparing the
for a piece of sophistry.
They are called

real life

way
"

"

because the predicate is obtained
by merely analysing the subject. Before the
time of Kant it was thought that all judgments
analytic

of

which we could be certain a

of this kind

:

that in

all

of

priori were

them there was a

predicate which was only part of the subject
of

which

it

was

asserted.

If this

were

so,

we

A PRIORI KNOWLEDGE
should

be

diction

if

involved

in

129

a definite contra-

we attempted to deny anything
known a priori. " A bald man

that could be
is

"

would assert and deny baldness
same man, and would therefore conThus according to the philoitself.

not bald

of the

tradict

sophers before Kant, the law of contradiction,
which asserts that nothing can at the same

time have and not have a certain property,
sufficed to establish the truth of all a priori
knowledge.

Hume

(1711-1776), who preceded Kant,
accepting the usual view as to what makes
knowledge a priori, discovered that, in many

had previously been supposed
analytic, and notably in the case of cause and
effect, the connection was really synthetic.
Before Hume, rationalists at least had
cases which

supposed that the effect could be logically
deduced from the cause, if only we had
sufficient

rectly,

—that



Hume

argued coras would now be generally admitted
knowledge.

Hence he
more doubtful proposition

this could not be done.

inferred the far

that nothing could be

known a

priori

about

130

THE PROBLEMS OF PHILOSOPHY

the connection of cause and effect.

Kant,

who had been educated in the rationahst
tradition, was much perturbed by Hume's
scepticism,

and endeavoured to

find

an answer

He

perceived that not only the connection of cause and effect, but all the propo-

to

it.

of

sitions

arithmetic

"
synthetic,"
propositions,
will

reveal

i.e.

geometry,

not analytic

no
the

and

analysis

of

:

in all these

the

subject

His stock

predicate.

are

in-

=

the proposition 7 + 5
12.
He pointed out, quite truly, that 7 and 5
have to be put together to give 12
the
stance was

:

is not contained in them, nor
of
even in the idea of adding them together.
Thus he was led to the conclusion that all

12

idea

pure mathematics, though a
thetic

;

and

this

problem of which

priori, is

syn-

conclusion raised a

new

he endeavoured to find

the solution.

The question which Kant put at the be"
How is
ginning of his philosophy, namely
pure mathematics possible

"

is an interand
difficult
to
which
one,
esting
every philosophy which is not purely sceptical must find
?

A PRIORI KNOWLEDGE
some

The

answer.

empiricists,

that

answer

of

131

the

pure

know-

mathematical

our

derived by induction from particular
instances, we have already seen to be inade-

ledge

is

quate, for two reasons first, that the validity
of the inductive principle itself cannot be
proved by induction ; secondly, that the
:

general propositions of mathematics, such as
" two and two
always make four," can obvi-

ously be known with certainty by consideration of a single instance, and gain nothing by
enumeration of other cases in which they

have been found to be

true.

Thus our

the

general propositions of
knowledge
mathematics (and the same applies to
for otherwise than
logic) must be accounted
our (merely probable) knowledge of emof

pirical generalisations

such as

"

all

men

are

mortal."

The problem
such knowledge
perience

is

through the fact that
general, whereas all ex-

arises
is

particular.

It

we should apparently be

seems strange that
able to

know some

truths in advance about particular things of

which we have as yet no experience

;

but

it

1S2

THE PROBLEMS OF PHILOSOPHY

cannot easily be doubted that logic and arithmetic will apply to such things. We do not

know who

will

be the inhabitants of London

but we know that
them and any other two of them

a hundred years hence

any two
will

of

make

four

;

them.

of

of anticipating facts

This apparent
about things of

power
which we have no experience
surprising.

is

certainly

Kant's solution of the problem,

though not valid

in

my opinion,

is

interesting.

however, very difficult, and is differently
understood by different philosophers. We
It

is,

can, therefore, only give the merest outline
of it, and even that will be thought mis-

leading

by

many

exponents

of

Kant's

system.

What Kant maintained was

that in

all

our

two elements to be
experience
distinguished, the one due to the object
"
{i.e. to what we have called the
physical
object"), the other due to our own nature.
We saw, in discussing matter and sensethere

are

data, that the physical object is different
from the associated sense-data, and that

the sense-data are to be regarded as resulting

A PRIORI KNOWLEDGE

1S3

from an interaction between the physical
So far, we are in
object and ourselves.

But what is distinctive of Kant is the way in which he apportions the shares of ourselves and the physical
agreement with Kant.

He considers that the
object respectively.
the
crude material given in sensation
colour, hardness, etc.





is

due to the object,

and that what we supply is the arrangement
in space and time, and all the relations between sense -data which result from comparison or from considering one as the cause
of

the

other

or

in

any other way.

chief reason in favour of this

view

is

His
that

we seem

to have a 'priori knowledge as to
time and causality and compariand
space
son,
of

but not as to the actual crude material

sensation.

that

We

anything

we

can be sure,
shall

he

says,

ever

experience
must show the characteristics affirmed of it

our a priori knowledge, because these
characteristics are due to our own nature,

in

and therefore nothing can ever come
our

experience

characteristic*.

without

acquiring

into

these

THE PROBLEMS OF PHILOSOPHY

134

The

physical object, which he calls the
*
he regards as essentially
thing in itself,"
unknowable what can be known is the object

*'

;

as

we have

the
ing

it

in experience,

which he

calls

"

The phenomenon, bephenomenon."
a joint product of us and the thing in

itself,

is

sure to have those characteristics

which are due to us, and is therefore sure to
conform to our a priori knowledge. Hence
this knowledge, though true of all actual and
possible experience, must not be supposed
to apply outside experience. Thus in spite
of the existence of a priori knowledge, we
cannot know anything about the thing in
itself or

about what

is

object of experience.
reconcile

not an actual or possible
In this way he tries to

and harmonise the contentions

of

the rationalists with the arguments of the
empiricists.

Apart from minor grounds on which
Kant's philosophy may be criticised, there is
"

"

* Kant's
is identical in definition
thing in itself
with the physical object, namely, it is the cause of sensaIn the properties deduced from the definition it is
tion.
not identical, since Kant held (in spite of some inconsistency as regards cause) that we can know that none of the

categories are applicable to the

"

thing in itself."

A PRIORI KNOWLEDGE

135

one main objection which seems fatal to any
attempt to deal with the problem of a priori

knowledge by
accounted for

his
is

The thing to be

method.

our certainty that the facts

must always conform to logic and arithmetic.
To say that logic and arithmetic are contributed by us does not account for this. Our
nature is as much a fact of the existing world
as anything, and there can be no certainty
that it will remain constant
It might happen,
.

Kant

right, that to-morrow our nature
would so change as to make two and two

if

is

become five. This possibility seems never
to have occurred to him, yet it is one which
utterly destroys the certainty and universality which he is anxious to vindicate for
arithmetical propositions.
It is true that this
is
inconsistent
with the
possibility, formally,

Kantian view

that

time

itself

is

a form

imposed by the subject upon phenomena,
so that our real Self is not in time and has
no to-morrow.

But he

will

still

have to

suppose that the time-order of phenomena
is determined by characteristics of what is

behind phenomena, and this
substance of our argument.

suffices for the

THE PROBLEMS OF PHILOSOPHY

186

Reflection, moreover, seems to
that,

if

there

is

make it clear

any truth in our arithmetical

they must apply to things equally
whether we think of them or not. Two
physical objects and two other physical
objects must make four physical objects, even
if
physical objects cannot be experienced.

beliefs,

To

assert this

is

certainly within the scope
state that two and

what we mean when we
two are four. Its truth is
of

as

the

truth

of

just as indubitable

the assertion

that

two

phenomena and two other phenomena make
four phenomena. Thus Kant's solution unduly limits the scope of a priori propositions,
in addition to failing in the attempt at explaining their certainty.
Apart from the special doctrines advocated

by Kant,

it

is

very

common among

philois
a
what
as
in
some
to
regard
priori
sophers
sense mental, as concerned rather with the

way we must

think than with any fact of the
We noted in the preceding
chapter the three principles commonly called
*'
laws of thought." The view which led to
outer world.

their being so

named

is

a natural one, but

A PRIORI KNOWLEDGE

137

there are strong reasons for thinking that it
erroneous.
Let us take as an illustra-

is

the

tion

law

of

This

contradiction.

is

form " Nothing
commonly
can both be and not be," which is intended
to express the fact that nothing can at once
have and not have a given quality. Thus,
for example, if a tree is a beech it cannot
stated in

also be not a beech

gular

it

;

the

my

if

table

is

rectan-

cannot also be not rectangular, and

so on.

Now what makes

it

natural to call this

principle a law of thought is that it is by
thought rather than by outward observation

we persuade ourselves of its necessary
truth.
When we have seen that a tree is a
we
do not need to look again in order
beech,
that

to ascertain whether

it is

also not a beech

;

makes us know that this is
But the conclusion that the law

thought alone

impossible.
of contradiction

is

theless erroneous.

we

a law of thought

What we

mind

is

so

made

that

the law of contradiction.

when

believe,

believe the law of contradiction,

that the

never-

is

it

must

is

not

believe

This belief

is

a

188

THE PROBLEMS OF PHILOSOPHY

subsequent result of psychological

The

contradiction.

contradiction

is

reflection,

belief in the

which presupposes the

belief

law

in the law

of

of

a belief about things, not

It is not, e.g., the
only about thoughts.
belief that if we think a certain tree is a

beech,

that

it

we cannot
is

at the

not a beech

;

same time
it

is

think

the belief

a beech, it cannot at
the same time be not a beech. Thus the
law of contradiction is about things, and not
that

if

the tree

is

and although belief
merely about thoughts
in the law of contradiction is a thought, the
;

law of contradiction

itself is

not a thought,

but a fact concerning the things in the world.
If this, which we believe when we believe the
law

of contradiction,

were not true of the

things in the world, the fact that we were
compelled to think it true would not save

the law of contradiction from being false
and this shows that the law is not a law of
;

thought.

A

similar

argument applies to any other

When we

judge that
two and two are four, we are not making a
a priori judgment.

A PRIORI KNOWLEDGE

139

judgment about our thoughts, but about all
actual or possible couples. The fact that
our minds are so constituted as to believe
that two and two are four, though

it is

true,

emphatically not what we assert when we
assert that two and two are four.
And no
is

fact

about the constitution of our minds

could
four.

make

it

true that

two and two are

Thus our a

priori knowledge, if it
not erroneous, is not merely knowledge
about the constitution of our minds, but
is

applicable to whatever the world may
contain, both what is mental and what is
is

non-mental.

The

seems to be that

fact

all

our a priori

knowledge is concerned with entities which
do not, properly speaking, exist, either in the
mental or in the physical world. These entities are such as can be named
by parts of
which
are
not
substantives
speech
they are
such entities as qualities and relations. Sup;

pose, for instance, that I

am

in

my

room.

I

and my room exists but does " in "
exist ?
Yet obviously the word " in " has
a meaning it denotes a relation which holds
exist,

;

;

140

THE PROBLEMS OF PHILOSOPHY

between

me and my

room.

This relation

we cannot say

something, although

that

is

it

same sense in which I and my
room exist. The relation " in " is something
which we can think about and understand,

exists in the

we could not understand

for, if

it,

not understand the sentence " I

room."

we could

am

in

my

Many

philosophers, following Kant,
have maintained that relations are the work
of the

mind, that things in themselves have
no relations, but that the mind brings them
together in one act of thought and thus produces the relations which it judges them to
have.

This view, however, seems open to objec-

which we urged before
Kant.
It seems plain that it is not
against
thought which produces the truth of the
"
I am in my room."
It may be
proposition

tions similar to those

true that an earwig is in my room, even
neither I nor the earwig nor any one else

aware

of this truth

;

if

is

for this truth concerns

only the earwig and the room, and does not

depend upon anything
as

we

shall tee

more

else.

Thus

fully in the

relations,

next chapter.

A PRIORI KNOWLEDGE
must be placed

in

a world which

mental nor physical.

This world


is

141
neither
of great

importance to philosophy, and in particular
to the problems of a priori knowledge. In the
next chapter we shall proceed to develop its
nature and its bearing upon the questions

with which we have been dealing.

CHAPTER IX
THE WORLD OF UNIVERSALS

At

the end of the preceding chapter we saw
that such entities as relations appear to have

some way different from
that of physical objects, and also different
from that of minds and from that of senseIn the present chapter we have to
data.
consider what is the nature of this kind of
being, and also what objects there are that
have this kind of being. We will begin with
a being which

is

in

the latter question.
The problem with which we are

cerned

is

a very old one, since

into philosophy

"

by

Plato.

it

now

con-

was brought

Plato's

"

theory

an attempt to solve this very
problem, and in my opinion it is one of the
most successful attempts hitherto made. The
of ideas

is

theory to be advocated in what follows
142

is

THE WORLD OF UNIVERSALS

143

modificalargely Plato's, with merely such
tions as time has shown to be necessary.

The way the problem arose for Plato was
more or less as follows. Let us consider, say,
such a notion as justice. If we ask ourselves
what

justice

is,

it is

considering this, that,

natural to proceed by
and the other just act,

with a view to discovering what they have in

common.

They must

some

in

all,

sense,

partake of a common nature, which will be
found in whatever is just and in nothing else.
This

common

they are

nature, in

all just, will

virtue

be justice

of

itself,

which

the pure

essence the admixture of which with facts of

produces the multiplicity of just
Similarly with any other word which

ordinary
acts.

life

be applicable to common facts, such as
"
The word will be
for example.
whiteness
applicable to a number of particular things

may
"

because they all participate in a common
nature or essence. This pure essence is what
"
""
"
form." (It must
idea
or
Plato calls an
"
not be supposed that
ideas," in his sense,
exist in minds,

though they

hended by minds.)

The

"

be apprejustice is not

may

idea

"

THE PROBLEMS OF PHILOSOPHY

144

identical with anything that

is

just

:

it is

some-

other than particular things, which

thing

particular

Not being
partake of.
cannot itself exist in the world

things

particular,

it

of

Moreover

sense.

changeable

like

it

not

is

or

fleeting

the things of sense

:

it

is

itself, immutable and indestructible.
Thus Plato is led to a supra-sensible world,
more real than the common world of sense,

eternally

the unchangeable world of ideas, which alone
gives to the world of sense whatever pale

may

reflection of reality

belong to

it.

The

truly real world, for Plato, is the world of
ideas

;

for

whatever we

attempt to say
we can

may

about things in the world

of sense,

only succeed in saying that they participate
in such and such ideas, which, therefore,
constitute

all

Hence

their character.

it

is

easy to pass on into a mysticism. We may
hope, in a mystic illumination, to see the ideas
as

we

see objects ot sense

;

and we may

in heaven.
imagine
These mystical developments are very natural,
but the basis of the theory is in logic, and it is

that

the

ideas

as based in logic that

exist

we have

to consider

it.

THE WORLD OF UNIVERSALS

145

" has
acquired, in the
course of time, many associations which are

The word

*'

idea

quite misleading when applied to Plato's
"
ideas."
We shall therefore use the word

"universal" instead of the word "idea," to
what Plato meant. The essence of

describe

the sort of entity that Plato meant is that it
is opposed to the particular things that are

given in sensation.
is

We

given in sensation, or

is

speak of whatever
of the same nature

as things given in sensation, as a particular

by

;

opposition to this, a universal will be any-

thing which
culars,

may be

shared by

and has those

many

parti-

characteristics which,

we saw,

distinguish justice and whiteness
from just acts and white things.

as

When we examine common
find that,

stand

for

broadly speaking,
particulars,

we
proper names
words,

while

other

,

;

sub'

stantives, adjectives, prepositions,

stand for universals.
particulars, but are

Pronouns

and verbs
stand

for

ambiguous it is only
the
context
or
the
circumstances that
by
we know what particulars they stand for.
The word " now " stands for a particular.
:



THE PROBLEMS OF PHILOSOPHY

146

namely the present moment but like pronouns, it stands for an ambiguous particular,
;

because the present is always changing.
It will be seen that no sentence can be

made up without

at least one

word which

The nearest approach
"
I like
would be some such statement as
"
"
this."
But even here the word like dedenotes a universal.

notes a universal, for I

may

and other people may

like things.

like other things,

truths involve universals, and
of

all

Thus

all

knowledge

truths involves acquaintance with uni-

versals.
1-

Seeing that nearly all the words to be
found in the dictionary stand for universals,
strange that hardly anybody except
students of philosophy ever realises that there

it

is

are such entities as universals.
naturally dwell

upon those words

We

do not

in a sentence

which do not stand for particulars and if we
are forced to dwell upon a word which stands
;

a universal, we naturally think of it as
standing for some one of the particulars that

for

come under the universal. When, for example,
we hear the sentence, " Charles I.'s head was

THE WORLD OF UNIVERSALS
we may

cut off,"
Charles

naturally enough think of
and of the

of Charles I.'s head,

I.,

operation of cutting
particulars

147

;

off his

head, which are

all

but we do not naturally dwell
meant by the word " head " or

upon what is
"
the word
cut," which is a universal. We
feel such words to be incomplete and insubstantial
they seem to demand a context
;

anything can be done with them.
Hence we succeed in avoiding all notice of
before

universals as such, until the study of philosophy forces them upon our attention.

Even among

we may

philosophers,

say,

broadly, that only those universals which are
named by adjectives or substantives have been

much

or often recognised, while those

named

by verbs and prepositions have been usually
overlooked. This omission has had a very
it is
great effect upon philosophy
hardly
too much to say that most metaphysics, since
;

Spinoza, has been largely determined by it.
The way this has occurred is, in outline, as
follows

:

common
of

single

Speaking generally, adjectives and
nouns express qualities or properties
things,

whereas prepositions and

148

THE PROBLEMS OF PHILOSOPHY

verbs tend to express relations between two
Thus the neglect of preor more things.
positions

and verbs

led to the belief that

every proposition can be regarded as attributing a property to a single thing, rather

than as expressing a relation between two or

Hence

was supposed that,
ultimately, there can be no such entities as
Hence either there
relations between things.

more

things.

it

can be only one thing in the universe, or, if
many things, they cannot possibly

there are

interact in

any way,

would be a

relation,

since

and

any interaction
relations are im-

possible.

The

first

of these views,

which was advo-

cated by Spinoza, and is held in our own day
by Mr. Bradley and many other philosophers,
is

called

monism

;

the second, which was

advocated by Leibniz, but is not very common
nowadays, is called monadism, because each
of the isolated things is called a monad. Both
these opposing

philosophies,

interesting as

result, in my opinion, from an undue
attention to one sort of universals, namely the

they are,

sort represented

by adjectives and substan-

THE WORLD OF UNI VERS ALS
tives

rather

than

149

by verbs and prepoji-

tions.

As a matter

of fact,

if

any one were anxious

to deny altogether that there are such things
as universals, we should find that we cannot
strictly

prove that there are such entities as

qualities,

i.e.

the universals represented by

adjectives and substantives, whereas
prove that there must be relations,

we can
i.e.

sort of universals generally represented

the

by

verbs and prepositions. Let us take in illustration the universal whiteness.
If we believe
is such a universal, we shall say
that things are white because they have the
quality of whiteness. This view, however,

that there

was strenuously denied by Berkeley and
Hume, who have been followed in this by
later

empiricists.

The

form

which

their

denial took was to deny that there are such
"
abstract ideas." When we want
things as
to think of whiteness, they said, we form an

image

of

some particular white

thing,

and

reason concerning this particular, taking care
not to deduce anything concerning it which

we cannot

see to be equally true of

any other

150

THE PROBLEMS OF PHILOSOPHY
As an account

white thing.

mental processes, this

of our actual

no doubt largely

is

In geometry, for example, when we
wash to prove something about all triangles,
we draw a particular triangle and reason about

true.

taking care not to use any characteristic
which it does not share with other triangles.
it,

The beginner,
finds

it

in order to avoid error, often

useful to

draw several

triangles, as

unlike each other as possible, in order to
make sure that his reasoning is equally applicable to

all of

as soon as

them.

we ask

But a

difficulty

emerges

how we know
a triangle. If we

ourselves

that a thing is white or
wish to avoid the universals whiteness and
triangularity,

we

some particular
some particular triangle,

shall choose

patch of white or

and say that anything

is

white or a triangle

has the right sort of resemblance to our
chosen particular. But then the resemblance

if it

required will have to be a universal. Since
there are many white things, the resemblance

must hold between many pairs of particular
white things
and this is the characteristic
;

of a universal.

It will

be useless to say that

THE WORLD OF UNIVERSALS
there

is

a different resemblance

for

151

each

pair, for then we shall have to say that these
resemblances resemble each other, and thus
at last we shall be forced to admit resem-

The relation of remust
be a true universal.
semblance, therefore,
And having been forced to admit this universal, we find that it is no longer worth
while to invent difficult and unplausible
blance as a universal.

theories to

avoid

the

universals as whiteness

Berkeley and

Hume

admission

and

of

triangularity.

failed

to

this refutation of their rejection of

perceive
"

abstract

ideas," because, like their adversaries,

only

thought

ignored

of

relations

such

they

and altogether
as universals.
We have
qualities,

therefore here another respect in which the
rationalists appear to have been in the right
as against the empiricists, although, owing
to the neglect or denial of relations, the

deductions

made by

rationalists were,

if

any-

more apt to be mistaken than those
made by empiricists.
Having now seen that there must be such

thing,

entities as universals, the

next point to be

THE PROBLEMS OF PHILOSOPHY

152

that their being is not merely mental.
this is meant that whatever being belongs

proved

By

is

them

independent of their being thought
of or or in any way apprehended by minds.

to

is

We

have already touched on this subject at
the end of the preceding chapter, but we
must now consider more fully what sort of
being it is that belongs to universals.
"
Consider such a proposition as
Edinburgh
is

Here we have a rebetween two places, and it seems plain

north of London."

lation

that the relation subsists independently of

our knowledge of it. When we come to know
that Edinburgh is north of London, we come
to

know something which

Edinburgh and London

:

has to do only with

we do not cause the
by coming to know

truth of the proposition
it, on the contrary we merely apprehend a
The
fact which was there before we knew it.
part of the earth's surface where Edinburgh
stands would be north of the part where

London

stands, even

even

if

if

there were no

know about north and

being to

there were no minds at

universe.

This

is,

human

south,
all

of course, denied

and

in the

by many

THE WORLD OF UNIVERSALS

153

philosophers, either for Berkeley's reasons
or for Kant's. Cut we have already con-

sidered these reasons,
are

nd decided that they

inadequate. We may therefore now
it to be true that nothing mental is

assume

presupposed in the fact that Edinburgh is
north of London. But this fact involves the
"

north of," which is a universal
and it would be impossible for the whole fact to

relation

;

"
north
involve nothing mental if the relation
of," which is a constituent part of the fact,
did involve anything mental. Hence we

must admit that the
it

relation, like the

terms

not dependent upon thought, but
to the independent world which

relates, is

belongs

thought apprehends but does not create.
This conclusion, however, is met by the
"
"
north of
does
difficulty that the relation
not seem to exist in the same sense in which

Edinburgh and London exist. If we ask
"
Where and when does this relation exist ? "
"
Nowhere and no when."
the answer must be
or
time where we can find
There is no place
the relation

"

north of."

It does not exist in

Edinburgh any more than in London, for

it

THE PROBLEMS OF PHILOSOPHY

154

two and

relates the

neutral as between

is

Nor can we say that

them.

Now

(particular time.

it

exists at

any

everything that can

be apprehended by the senses or by intro:spection

exists

Hence the
different

at

relation

from

some
"

particular

north of

such things.

"
It

is

time.

radically

is

neither

in space nor in time, neither material nor

mental
It

is

;

yet

it is

largely

something.
the very peculiar kind of

being that belongs to universals which has led
many people to suppose that they are really
mental.

We

can think

of

a universal, and our

thinking then exists in a perfectly ordinary
sense, like any other mental act. Suppose, for

example, that we are thinking of whiteness.
Then in one sense it may be said that white"
We have here the
in our mind."
ness is

same ambiguity as we noted

in discussing

Chapter IV. In the strict sense,
not whiteness that is in our mind, but the

Berkeley in
it is

act of thinking of whiteness. The connected
"
idea," which we
ambiguity in the word

noted at the same time, also causes confusion
In one sense of this word, namely the
here.

THE WORLD OF UNIVERSALS

155

denotes the object of an act
"
idea." Hence,
of thought, whiteness is an
if the ambiguity is not guarded against, we
sense in which

may come
"

"

it

to

think that whiteness

is

an

i.e. an act of
to think that
and
thus
we
come
thought
whiteness is mental. But in so thinking, we

idea

in the other sense,

;

rob

it

of its essential quality of universality.

One man's act

of thought is necessarily a
one
from
another man's
thing
man's act of thought at one time is necessarily a different thing from the same man's

different

;

act of thought at another time. Hence, if
whiteness were the thought as opposed to its

no two different men could think of it,
and no one man could think of it twice.
That which many different thoughts of whiteness have in common is their object, and this
object is different from all of them. Thus
object,

not thoughts, though when
are the objects of thoughts.
shall find it convenient only to speak

universals

are

known they

We

when they are in time, that
when we can point to some time ai

of things existing
is

to say,

which they exist (not excluding the

possi-

156

THE PROBLEMS OF PHILOSOPHY

bility of their existing at all times).

thoughts and
objects exist.
in this sense

;

Thus*

feelings, minds and physical
But universals do not exist

we

shall say that

"

they subsist

"

or have being, where
is opposed to
being
*'
"
existence
as being timeless.
The world
of universals, therefore,

may

as the world of being.

also be described

The world

of being

is unchangeable, rigid, exact, delightful to
the mathematician, the logician, the builder

metaphysical systems, and all who love
The world of
perfection more than life.

of

existence

is

vague, without

sharp
boundaries, without any clear plan or arrangement, but it contains all thoughts and feelings,
fleeting,

the data of sense, and

all physical objects,
do
that
can
either
good or harm,
everything
everything that makes any difference to the
all

value of

life

and the world.

According to

our temperaments, we shall prefer the contemplation of the one or of the other. The

one we do not prefer will probably seem to us
a pale shadow of the one we prefer, and hardly

worthy to be regarded as in any sense real.
But the truth is that both have the same

THE WORLD OF UNIVERSALS

157

cairn on our impartial attention, both are
real, and both are important to the meta-

Indeed no sooner have we

physician.

dis-

tinguished the two worlds than it becomes
necessary to consider their relations.

But

first

knowledge

of

all

we must examine our

of universals.

This consideration

occupy us in the following chapter,
where we shall find that it solves the problem
of a priori knowledge, from which we were
will

first

led to consider universals.

CHAPTER X
ON OUR KNOWLEDGE OF UNIVERSALS
In regard to one man's knowledge at a
given time, universals, like particulars, may
be divided into those known by acquaintance,
those known only by description, and those

not

known

either

by acquaintance

or

by de-

scription.

Let us consider
universals

the knowledge of

first

by acquaintance.

It is obvious,

to begin with, that we are acquainted with
such universals as white, red, black, SAveet,
loud,

sour,

hard,

i.e.

etc.,

with qualities

which are exemplified in sense-data.

we
in

are acquainted,
see a white patch,
the first instance, with the particular

white patches,
easily learn to abstract the whiteness

patch

we

When

we

;

but by seeing

which they

all

have

many

in

158

common, and

in

ON KNOWLEDGE OF UNIVERSALS
learning to

do

this

we

159

are learning to be

acquainted with whiteness. A similar process will make us acquainted with any
other universal of the same sort,
"

of this sort
ties."

may

be called

Universals

sensible quali-

They can be apprehended with

less

of abstraction than any others, and
seem
less removed
from particulars
they
than other universals are.
We come next to relations. The easiest
effort

apprehend are those which hold
between the different parts of a single complex
sense-datum. For example, I can see at a
relations to

glance the whole of the page on which I am
writing ; thus the whole page is included in

But I perceive that some
are
to the left of other parts,
page
parts are above other parts. The

one sense-datum.
parts of the

and some

process of abstraction in this case seems to
proceed somewhat as follows I see success:

ively a number of sense-data in which one
part is to the left of another I perceive, as in
;

the case of different white patches, that all
these sense-data have something in com-

mon, and by abstraction

I find that

what

THE PROBLEMS OF PHILOSOPHY

ICO

they have in common is a certain relation
between their parts, namely the relation
"
which I call
In
being to the left of."
this

way

I

become acquainted with the

universal relation.

In like manner I become aware of the
relation of before
I

and

after in time.

hear a chime of bells

:

when

Suppose

the last bell of

the chime sounds, I can retain the whole

chime before

mind, and I can perceive

my

that the earlier bells

Also

ones.

what

am

I

in

came before the
I

memory

later

perceive that
before the

remembering came

present time. From either of these sources
I can abstract the universal relation of be-

and

fore

universal

after,

Thus time
are

just

relation
-

among

as

I

abstracted

"being to the

left

the
of."

space relations,
those with which we are ac-

relations,

like

quainted.

Another relation with which we become
acquainted in much the same way is resemof green, I

other

;

simultaneously two shades
can see that they resemble each
also see a shade of red at the same

If I see

blance.

if

I

ON KNOWLEDGE OF UNIVERSALS

161

that the two greens have
more resemblance to each other than either
time, I can

see

has to the red.

In

this

way

I

become

acquainted with the universal resemblance or
similarity.

Between

as

between

parti-

culars, there are relations of

which we

may be

universals,

immediately aware. We have just seen that
we can perceive that the resemblance between

two shades of green is greater than the resemblance between a shade of red and a shade
of green.
Here we are dealing with a relation,
"
namely
greater than," between two relations.
Our knowledge of such relations,
though it requires more power of abstraction
than

required for perceiving the qualities
of sense-data, appears to be equally immediate,

and

is

(at least in

able.

some

Thus there

is

cases) equally indubit-

immediate knowledge

concerning universals as well as concerning
sense-data.

Returning now to the problem of a priori
knowledge, which we left unsolved when we

began the consideration of universals, we find
ourselves in a position to deal with it in a
F

THE PROBLEMS OF PHILOSOPHY

162

much more

satisfactory manner than was
Let us revert to the propossible before.
"
two
and
two are four." It is
position

obvious, in view

fairly

of

what has been

that this proposition states a relation
"
between the universal
two " and the uni-

said,

versal "four."

which we
blish

;

now endeavour

to

esta-

namely, All a priori knowledge deals

exclusively

This

This suggests a proposition

shall

with

the

proposition

relations

is

of

great

of

universals.

importance,

and goes a long way towards solving our
previous difficulties concerning a priori knowledge.

The only case

in which it might seem, at
our proposition were untrue,
the case in which an a priori proposition

first sight,
is

as

if

one class of particulars
belong to some other class, or (what comes to
states that

all of

the same thing) that

all particulars

having

some one property also have some other. In
this case it might seem as though we were
dealing with the particulars that have the
property rather than with the property. The
"
two and tv»o are four " is really
proposition

ON KNOWLEDGE OF UNIVERSALS

163

a case in point, for this may be stated in the
form " any two and any other two are four,"
"
or
any collection formed of two twos is a
collection of four."

If

we can show

that

such statements as this really deal only with
universals, our proposition may be regarded
as proved.

One way

what a proposition
deals with is to ask ourselves what words we
must understand in other words, what obin order
jects we must be acquainted with
to see what the proposition means. As soon
as we see what the proposition means, even
of discovering





if

we do not yet know whether it is true
it is evident that we must
have

or false,

acquaintance with whatever is really dealt
with by the proposition. By applying this
test,

it

appears that

many

propositions

which might seem to be concerned with particulars are really concerned only with uni"
In the special case of
versals.
two and

two are four," even when we interpret it as
"
meaning any collection formed of two twos
a collection of four," it is plain that we
can understand the proposition, i.e. we can
is

THE PROBLEMS OF PHILOSOPHY

164
see

what

it is

know what

is

"

"

two

"

and

that

it

asserts, as

meant by "

soon as w«
"

and

collection

four."
It is quite unnecessary
the couples in the world
if it
were necessary, obviously we could never

to

know

all

:

understand the proposition, since the couples
are infinitely numerous and therefore cannot
all

be known to us

.

Thus although our general

statement implies statements about particular couples, as soon as we know that there are
such particular couples, yet it does not itself
assert or imply that there are such particular

and thus fails to make any statement
whatever about any actual particular couple.

couples,

The

statement

made

the universal, and not

is

about

about

"couple,"

this or that

couple.

Thus the statement " two and two are four **
deals exclusively with universals, and therefore
be known by anybody who is acquainted
with the universals concerned and can per-

may

them which the
statement asserts. It must be taken as a
fact, discovered by reflecting upon our knowledge, that we have the power of sometimes

ceive the relation between

ON KNOWLEDGE OF UNIVERSALS

165

perceiving such relations between universals,

and therefore

sometimes knowing general
a priori propositions such as those of arithmetic and logic. The thing that seemed
mysterious,

of

when we formerly considered such

knowledge, was that

it

seemed to anticipate

and control experience. This, however, we
can now see to have been an error. No fact
concerning anything capable of being experienced can be
experience.

known independently

of

We know a priori that two things

and two other things together make four
things, but we do not know a priori that if
Brown and Jones are two, and Robinson and
Smith are two, then Brown and Jones and
Robinson and Smith are four. The reason is
that this proposition cannot be understood
at all unless we know that there are such

Brown and Jones and Robinson
and Smith, and this we can only know by
people as

experience.
is

Hence, although our general
a priori, all its applications

proposition
to actual particulars involve experience and
In
therefore contain an empirical element.
this

way what seemed mysterious

in our a

THE PROBLEMS OF PHILOSOPHY

166

knowledge
an
error.
upon
priori

is

seen to have been based

It will serve to make the point clearer if we
contrast our genuine a priori judgment with an
"
empirical generalisation, such as all men are

mortals." Here as before, we can understand
what the proposition means as soon as we
understand the universals involved, namely
man and mortal. It is obviously unnecessary
to have an individual acquaintance with the

whole human race in order to understand

what our proposition means. Thus the difference between an a priori general proposition

and an empirical generalisation does

not come in the meaning of the proposition
it comes in the nature of the evidence for it.
;

In the empirical case, the evidence consists
in

the

that

all

We

particular instances.
men are mortal because

believe

we know

that there are innumerable instances of

men

dying, and no instances of their living beyond a certain age. We do not believe it

because

we

universal
is

see a connection

man and

true that

if

between the

the universal mortal.

It

physiology can prove, assum-

ON KNOWLEDGE OF UNIVERSALS

1G7

ing the general laws that govern living bodies,
that no living organism can last for ever, that
gives a connection between man and mortality
which would enable us to assert our proposition without appealing to the special evidence

But that only means that our
has
been subsumed under a
generalisation
wider generalisation, for which the evidence
of

men

dying.

is

still

of the

sive.

same kind, though more exten-

The progress

of science

is

constantly

producing such subsumptions, and therefore
giving a constantly wider inductive basis
for scientific generalisations.

But although

a greater degree of certainty, it
does not give a different kind the ultimate
ground remains inductive, i.e. derived from
this gives

:

instances,

and not an a

of universals such as

priori connection

we have

in logic

and

arithmetic.

Two

opposite points are to be observed
concerning a priori general propositions. The
particular instances are
known, our general proposition may be arrived
at in the first instance by induction, and the
first is

that,

if

many

connection of universals

may

be only sub-

THE PROBLEMS OF PHILOSOPHY

168

sequently perceived. For example, it is known
that if we draw perpendiculars to the sides of

a triangle from the opposite angles, all three
perpendiculars meet in a point. It would be
quite possible to be

first

led to this proposition

by

actually drawing perpendiculars in many
cases, and finding that they always met in a

point

;

this experience

for the general proof

are

might lead us to look
find it.
Such cases

and

common in the experience of every mathe-

matician.

The other point is more interesting, and of
more philosophical importance. It is, that

we may sometimes know a general proposition
in cases where we do not know a single inTake such a case as the following
numbers can be
and
will
give a third
multiplied together,
stance of it.

We know

:

that any two

called their product.

We know

of integers the product of

that

which

all

is less

pairs

than

100 have been actually multiplied together,
and the value of the product recorded in the
multiplication table. But we also know that
the number of integers is infinite, and that
only a finite number of pairs of integers ever

ON KNOWLEDGE OF UNIVERSALS
have been or ever

Hence

beings.

will

be thought of by

human

follows that there are pairs

which never have been and never

of integers
will

it

169

be thought of by human beings, and that
them deal with integers the product of

all of

which

is

over 10(^
"

proposition

:

Hence we

All products of

arrive at the

two

which never have been and never
thought of

Here

is

truth

is

integers,
will

be

by any human being, are over 100."

a general proposition of which the
undeniable, and yet, from the very

nature of the case,

we can never

give an in-

because any two numbers we may
think of are excluded by the terms of the
stance

;

proposition.

This possibility, of knowledge of general
propositions of which no instance can be given,
is

often denied, because

it

is

not perceived

that the knowledge of such propositions only
requires a knowledge of the relations of universals, and does not require any knowledge of
instances of the universals in question. Yet

the knowledge of such general propositions
is quite vital to a great deal of what is
generFor example, we
ally admitted to be known.

170

THE PROBLEMS OF PHILOSOPHY

saw,

in

our early chapters, that physical

opposed to sense-data, are only
obtained by an inference, and are not things
with which we are acquainted. Hence we
can never know any proposition of the form
"
"
"
this is a physical object," where
this
is
objects, as

something immediately known. It follows
that all our knowledge concerning physical
objects is such that no actual instance can be

We

can give instances of the associated sense-data, but we cannot give instances

given.

of the actual physical objects.

Hence our

knowledge as to physical objects depends
throughout upon this possibility of general
knowledge where no instance can be given.

And

the same applies to our knowledge of
other people's minds, or of any other class of
things of which no instance is known to us by
acquaintance.

We may now

take a survey of the sources
our knowledge, as they have appeared
We have
in the course of our analysis.

of

to distinguish knowledge of things
knowledge of truths. In each there are
first

kinds,

and
two

one immediate and one derivative.

ON KNOWLEDGE OF UNIVERSALS
Our immediate knowledge

of things,

171

which we

acquaintance, consists of two sorts,
according as the things known are particulars
or universals.
Among particulars, we have
called

acquaintance with sense-data and (probably)
with ourselves. Among universals, there seems
to be

no principle by which we can decide

which can be known by acquaintance, but it
is clear that among those that can be so known
are sensible qualities, relations of space and
time, similarity, and certain abstract logical

Our
which we

universals.
things,

derivative
call

knowledge

of

knowledge by descripboth acquaintance

involves

always
with something and knowledge of truths.
Our immediate knowledge of truths may be

tion,

called intuitive knowledge,

known may be

Among

called

and the truths

self-evident

so

truths.

such truths are included those which

merely state what

is

given in sense, and also

certain abstract logical

and arithmetical

prin-

and (though with less certainty) some
ethical propositions.
Our derivative know-

ciples,

ledge of truths consists of everything that
we can deduce from self-evident truths

THE PROBLEMS OF PHILOSOPHY

172

by the use

of

self

-

evident

principles

of

deduction.
If the

,

above account is

correct, all our

know-

If

ledge of truths depends

upon our intuitive

becomes important
and scope of intuitive
knowledge, in much the same way as, at an
earlier stage, we considered the nature and
scope of knowledge by acquaintance. But
knowledge.

It therefore

to consider the nature

knowledge of truths raises a further problem,
which does not arise in regard to knowledge
of things,

namely the problem

of error.

Some

and
becomes necessary to consider
at all, we can distinguish knowledge

of our beliefs turn out to be erroneous,

therefore

how,
from

if

it

error.

This problem

does

not

arise

with regard to knowledge by acquaintance,
for, whatever may be the object of acquaintance, even in dreams

and hallucinations, there

no error involved so long as we do not go
beyond the immediate object error can only
arise when we regard the immediate object,
is

:

mark of some
Thus
the
physical object.
problems connected with knowledge of truths arc more

i.e.

the sense-datum, as the

ON KNOWLEDGE OF UNIVERSALS
difficult

173

than those connected with know-

As the

the problems
connected with knowledge of truths, let us
examine the nature and scope of our intuiledge of things.

tive judgments.

first of

CHAPTER XI
ON INTUITIVE KNOWLEDGE

common impression that everything that we believe ought to be capable of
proof, or at least of being shown to be highly
There

probable.
for

a

is

It is felt

by many that a

which no reason can be given

reasonable belief.
just.

Almost

all

is

belief

an un-

In the main, this view

our

common

beliefs

is

are

either inferred, or capable of being inferred,

from other

beliefs which may be regarded as
the
for them.
reason
As a rule, the
giving
reason has been forgotten, or has even never

been consciously present to our minds. Few
of us ever ask ourselves, for example, what
to suppose the food we are just
going to eat will not turn out to be poison.
Yet we feel, when challenged, that a perfectly

reason there

is

good reason could be found, even
174

if

we

are

ON INTUITIVE KNOWLEDGE
not ready with
this belief

we

it

at the

175

And

moment.

in

are usually justified.

us imagine some insistent Socrates,
who, whatever reason we give him, continues
to demand a reason for the reason. We must

But

let

sooner or later, and probably before very long,
be driven to a point where we cannot find any
further reason, and where it becomes almost
certain that no further reason

discoverable.

retically

is

Starting

even theowith

the

we can be driven
backfrom point to point, until we come to some

common

beliefs of daily life,

general principle, or

some instance

of

a general

which seems luminously evident,
and is not itself capable of being deduced
from anything more evident. In most questions of daily life, such as whether our food is

principle,

be nourishing and not poisonous, we
shall be driven back to the inductive principle,

likely to

which we discussed in Chapter VI. But beyond that, there seems to be no further
regress.

The principle itself is constantly used

in our reasoning,

sometimes consciously, somebut there is no reasoning

times unconsciously

;

which, starting from some simpler self-evident

176

THE PROBLEMwS OF PHILOSOPHY

principle, leads us to the principle of induction
And the same holds for
as its conclusion.

other logical principles.
to us, and we employ

them

in constructing

but they themselves, or at
of
them, are incapable of

demonstrations

some

least

Their truth is evident

;

demonstration.
Self-evidence, however,

those

among

general

is

principles

When

incapable of proof.

not confined to

which are

a certain number

have been admitted, the
from them
but the
deduced
rest can be
propositions deduced are often just as selfevident as those that were assumed without
of logical principles

;

proof.

All

arithmetic,

moreover,

deduced from the general principles

can

be

of logic,

yet the simple propositions of arithmetic,
"
two and two are four," are just
such as
as self-evident as the principles of logic.

though this is more
disputable, that there are some self-evident
"
we ought to
ethical principles, such as
pursue what is good."
It

would seem,

It should

also,

be observed that, in

all

casei of

general principles, particular instances, dealing

ON INTUITIVE KNOWLEDGE

177

with familiar things, are more evident than
general principle. For example, the

the

law of contradiction states that nothing can
both have a certain property and not have
it.

This

but

it is

rose which

not red.

evident as soon as

understood,
not so evident as that a particular

is

we

it is

see cannot be both red

(It is of

and

course possible, that parts

may be red and parts not red,
or that the rose may be of a shade of pink
which we hardly know whether to call red
of the rose

or not

;

but in the former case

the rose as a whole
latter case the

as soon as

is

answer

it is

plain that

not red, while in the
is

theoretically definite

we have decided on a

precise de-

"

red.") It is usually through
that we come to be able
instances
particular
to see the general principle.
Only those
finition

who

of

are practised in dealing with abstractions

can readily grasp a general principle without
the help of instances.
In addition to general principles, the other
kind of self-evident truths are those imme-

We

will call
diately derived from sensation.
"
truths of perception," and the
such truths

THE PROBLEMS OF PHILOSOPHY

178

judgments
"

of

judgments

certain

them we will call
perception." But here a

expressing

amount

of care

is required in getof the truths that
nature
ting at the precise

The actual sense-data

are self-evident.

A

neither true nor false.

which

colour
exists

it

:

is

true or false.

are

particular patch of

I see, for example, simply
not the sort of thing that is
It is true that there is such

has a certain shape and
degree of brightness, true that it is surrounded
by certain other colours. But the patch

a patch, true that

itself,

like

sense,

is

of

it

everything else in the world of
a radically different kind from

the things that are true or false, and therefore
cannot properly be said to be true. Thus

whatever

self-evident

truths

be

may

obtained from our senses must be different

from the sense-data from which they are
obtained.
It

would seem that there are two kinds

self-evident

truths

of

coalesce.

First,

though
two kinds

perception,

perhaps in the last analysis the

may

of

there

which simply asserts the

is

the

existence

of

kind
the

ON INTUITIVE KNOWLEDGE

179

sense-datum, without in any way analysing
We see a patch of red, and we judge
"
there is such-and-such a patch of red," or
"
this is one
more strictly " there is that
it.

;

kind of intuitive judgment of perception.
The other kind arises when the object of
sense

is

complex, and we subject

degree of analysis.

If,

a round patch of red, we
patch of red is round."

judgment

to

it

for instance,

of perception,

may
This

but

it

"

judge
is

some

we

see

that

again a

differs

from

our previous kind. In our present kind we
have a single sense-datum which has both
colour and shape
the shape is round.

is red and
Our judgment analyses
the datum into colour and shape, and then
recombines them by stating that the red
:

colour

is

the colour

round in shape. Another example
"
this is to the
judgment is
"
"
"
"
this
and
that
that," where

of this kind of

right of

seen simultaneously. In this kind of
judgment the sense-datum contains con-

are

which have some relation to each
and
the judgment asserts that these
other,
constituents have this relation.
stituents

180

THE PROBLEMS OF PHILOSOPHY

Another

class of intuitive judgments, ana-

logous to those of sense and yet quite distinct from them, are judgments of memory.
is some danger of confusion as to the
nature of memory, owing to the fact that
memory of an object is apt to be accompanied

There

by an image of the object, and yet the image
cannot be what constitutes memory. This
is

easily seen

image

by merely noticing that the
present, whereas what is

in the

is

remembered is known to be in the past. Moreover, we are certainly able to some extent
to compare our image with the object remembered, so that we often know, within
somewhat wide limits, how far our image is
but this would be impossible,
accurate
;

unless the object, as opposed to the image,
were in some way before the mind. Thus

the essence of

memory

is

not constituted by

the image, but by having immediately before
the mind an object which is recognised as
But for the fact of memory in this
past.
sense,

we should not know

that there evei

was a past at all, nor should we be able to
"
understand the word
past," any more than

ON INTUITIVE KNOWLEDGE
a
"

man born

blind can understand the word

Thus there must be

light."

181

intuitive judg-

ments of memory, and it is upon them, ultimately, that all our knowledge of the past
depends.
The case of memory, however, raises a
difficulty, for it is notoriously fallacious,

and

thus throws doubt on the trustworthiness of

judgments in general.
no light one. But let us

This

intuitive

culty

is

first

diffi-

narrow

scope as far as possible.

Broadly speaking,
trustworthy in proportion to the
vividness of the experience and to its near-

its

memory

is

ness in time.

If

the house next door was

by lightning half a minute ago, my
memory of what I saw and heard will be so
reliable that it would be preposterous to
doubt whether there had been a flash at all.
And the same applies to less vivid experiences,
struck

so long as they are recent.

I

am

certain that half a minute ago I

absolutely

was

sitting

same chair in which I am sitting now.
Going backward over the day, I find things
of which I am quite certain, other things of

in the

which

I

am

almost certain, other things of

THE PROBLEMS OF PHILOSOPHY

182

can become certain by thought and
by calHng up attendant circumstances, and
some things of which I am by no means

which

I

I am quite certain that I ate my
certain.
breakfast this morning, but if I were as
indifferent to my breakfast as a philosopher
should be, I should be doubtful. As to the

conversation at breakfast, I can recall some
effort, some only
of
element
with a large
doubt, and some not
at all. Thus there is a continual gradation

of

it easily,

some with an

what

I

remember, and a corresponding gradation

in

in

the degree

of

self-evidence

the trustworthiness of

Thus the
fallacious

first

my

memory.

answer to the

memory

is

of

difficulty of

to say that

memory

has degrees of self-evidence, and that these
correspond to the degrees of its trustworthiness, reaching a limit of perfect self-evidence

and

perfect trustworthiness in our memory
of events which are recent and vivid.

would seem, however, that there are
cases of very firm belief in a memory which
It

is

wholly

cases,

false.

what

is

It is probable that, in these

really

remembered, in the

ON INTUITIVE KNOWLEDGE

183

sense of being immediately before the mind,
is
something other than what is falsely

though something generally associated with it, George IV. is said to have at
last believed that he was at the battle of

believed

in,

Waterloo, because he had so often said that
he was. In this case, what was immediately

remembered was his repeated assertion the
belief in what he was asserting (if it existed)
;

would be produced by association with the
remembered assertion, and would therefore
not be a genuine case of memory. It would
seem that cases of fallacious memory can
probably all be dealt with in this way, i.e.
they can be shown to be not cases of memory
in the strict sense at

is
is,

all.

One important point about self-evidence
made clear by the case of memory, and that
that self-evidence has degrees:

it is

not

a quality which is simply present or absent,
but a quality which may be more or less
from absolute
present, in gradations ranging

down

an almost imperceptible
Truths of perception and some of
faintness.
the principles of logic have the very highest

certainty

to

184

THE PROBLEMS OF PHILOSOPHY

truths of immediate
degree of self-evidence
memory have an almost equally high degree.
The inductive principle has less self-evidence
;

than some of the other principles oi logic,
such as *' what follows from a true premiss
must be true." Memories have a diminishing self-evidence as they become remoter and
fainter
the truths of logic and mathematics
;

have (broadly speaking) less self-evidence as
they become more complicated. Judgments
of intrinsic ethical or aesthetic value are apt

to have some self-evidence, but not much.

Degrees of self-evidence are important in
the theory of knowledge, since, if propositions

may

(as

seems

likely)

have some degree

of self -evidence without being true,

not be necessary to abandon

all

it

will

connection

between self-evidence and truth, but merely
to say that, where there is a conflict, the

more self-evident proposition is to be retained
and the less self-evident rejected.
seems, however, highly probable that
two different notions are combined in " self"
evidence
as above explained
that one of
them, which corresponds to the highest
It

;

ON INTUITIVE KNOWLEDGE

185

degree of self-evidence, is really an infallible
guarantee of truth, while the other, which

corresponds to all the other degrees, does
not give an infallible guarantee, but only a
greater or less presumption. This, however,

only a suggestion, which we cannot as yet
develop further. After we have dealt with
is

the nature of truth,

we

shall return to the

subject of self -evidence, in connection with
the distinction between knowledge and error.

CHAPTER

XII

TRUTH AND FALSEHOOD

Our knowledge

of

unlike

truths,

of things, has

our

an opposite, namely

knowledge
So far as things are concerned, we may
error.
know them or not know them, but there is no
positive state of mind which can be described
as erroneous knowledge of things, so long, at
any rate, as we confine ourselves to knowledge

acquaintance. Whatever we
quainted with must be something

are

by

:

ac-

we may

draw wrong inferences from our acquaintance,
but the acquaintance

cannot be decepno dualism as regards
itself

Thus there is
acquaintance. But as regards knowledge

tive.

truths, there

what

is

is

a dualism.

false as well

as

know

We may

what

is

of

believe

true.

We

that on very many subjects different people hold different and incompatible
186

TRUTH AND FALSEHOOD

187

hence some oeliefs must be erroopinions
neous. Since erroneous beliefs are often held
:

just as strongly as true beliefs,

it

becomes

question how they are to be distinguished from true beliefs. How are we to
know, in a given case, that our belief is not

a

difficult

erroneous

?

This

is

a question of the very

greatest difficulty, to which

no completely

There is,
satisfactory answer is possible.
a
however,
preliminary question which is
rather less difficult, and that is
What do we
:

viean

by

truth and falsehood

preliminary question which

is

?

It

this

is

to be considered

in this chapter.

In this chapter we are not asking

can know whether a
are asking

whether a

what

is

how we
we

belief is true or false

:

meant by the question

belief is true or false.

It

is

to be

hoped that a

clear answer to this question
us
to
obtain an answer to the quesmay help
tion what beliefs are true, but for the present
"
we ask only What is truth ? " and " What
" not "
is falsehood ?
What beliefs are true ? "
"
and
What beliefs are false ? " It is very

important to keep these different questions

188

THE PROBLEMS OF PHILOSOPHY
any confusion between
sure to produce an answer which is

entirely separate, since

them

is

not really applicable to either.
There are three points to observe in the

attempt to discover the nature of truth, three
requisites which any theory must fulfil.
(1)

admit

Our theory
of

its

of truth

opposite,

must be such as to

falsehood.

A

good

philosophers have failed adequately to
satisfy this condition
they have constructed

many

:

theories according to which all our thinking
ought to have been true, and have then had

the greatest difficulty in finding a place for
falsehood.
In this respect our theory of
belief must differ from our theory of acquaintance, since in the case of

acquaintance

was not necessary to take account

of

it

any

opposite.
(2) It

were no

seems

beliefs there could

and no truth
truth

is

fairly evident that

if

be no falsehood,

either, in the sense in

correlative

to

there

falsehood.

which
If

we

imagine a world of mere matter, there would
be no room for falsehood in such a world,

and although

it

would contain what may be

TRUTH AND FALSEHOOD
"

189

would not contain any
truths, in the sense in which truths are things
of the same kind as falsehoods.
In fact,
truth and falsehood are properties of beliefs
and statements
hence a world of mere
it
since
would
contain no beliefs or
matter,
statements, would also contain no truth or
called

it

facts,"

:

falsehood.

But, as against what we have just said,
to be observed that the truth or falsehood

(3)
it is

of

a belief always depends upon something
lies outside the belief itself.
If I be-

which

lieve that Charles

I.

died on the scaffold, I

believe truly, not because of any intrinsic
quality of my belief, which could be dis-

covered by merely examining the belief, but
because of an historical event which happened

two and a

half centuries ago.

that Charles
falsely

:

I.

If I believe

died in his bed, I believe

no degree

of vividness in

my

belief,

from
it, prevents
again because of what happened
long ago, and not because of any intrinsic
property of my belief. Hence, although truth
or of care in arriving at

being

it

false,

and falsehood are properties

of beliefs, they

190

THE PROBLEMS OF PHILOSOPHY

are properties dependent upon the relations
of the behefs to other things, not upon any
internal quality of the beliefs.
The third of the above requisites leads us to



adopt the view which has on the whole
been commonest among philosophers that



truth consists in some form of correspondence

between

belief

and

fact.

It

is, however, by
no means an easy matter to discover a form
of correspondence to which there are no
irrefutable objections.
By this partly and



partly

by the

feeling that,

if

truth consists

in a correspondence of thought with some-

thing outside thought, thought can never
know when truth has been attained many



philosophers have been led to try to find some
definition of truth which shall not consist in
relation to something wholly outside belief.

The most important attempt
of this sort

is

in coherence.

at a definition

the theory that truth consists
It is said that the mark of

failure to cohere in the body of
and that it is the essence of a
truth to form part of the completely rounded
system which is The Truth.

falsehood

our

is

beliefs,

TRUTH AND FALSEHOOD
There

is,

19i

however, a great difficulty in this

view, or rather two great difficulties. The
first is that there is no reason to suppose that

only one coherent body of beliefs is possible.
It may be that, with sufficient imagination, a

might invent a past for the world
that would perfectly fit on to what we know,
and yet be quite different from the real past.
novelist

In more

scientific matters, it is certain that

there are often two or more hypotheses which
account for all the known facts on some sub-

and although, in such cases, men of
science endeavour to find facts which will

ject,

rule out all the hypotheses except one, there
is no reason why they should always succeed.

In philosophy, again,

common

for

two

it

seems not un-

hypotheses to be both
the facts. Thus, for
possible that life is one long
rival

able to account for

all

example, it is
dream, and that the outer world has only that

degree of reality that the objects of dreams
but although such a view does not
have
;

seem inconsistent with known facts, there is
no reason to prefer it to the common-sense
view, according to which other people and

THE PROBLEMS OF PHILOSOPHY

192

things do really exist.
the definition of truth

Thus coherence as
fails

because there

is

no proof that there can be only one coherent
system.

The other objection
truth

is

to this definition of
"

assumes the meaning of co"
coherknown, whereas, in fact,

that
"

it

herence
"
ence
presupposes the truth of the laws of
Two propositions are coherent when
logic.

be true, and are incoherent when
one at least must be false. Now in order to

both

may

know whether two propositions can both be
true, we must know such truths as the law
contradiction.
For example, the two
"
"
and
this
tree is a beech
propositions
"
this tree is not a beech," are not coherent,
of

because of the law of contradiction.
if

the law of contradiction

itself

jected to the test of coherence,

else.

were sub-

we should

find

we choose

to suppose it false, nothing
be
incoherent with anything
any longer

that,
will

But

if

Thus the laws

of

logic

supply the

skeleton or framework within which the test
of coherence

applies,

and they themselves

cannot be established by this

test.

TRUTH AND FALSEHOOD
For the above two reasons,

198

coherence

cannot be accepted as giving the meaning of
truth, though it is often a most important
test

of truth after

a certain amount of truth

has become known.

Hence we are driven back to correspondence
with fact as constituting the nature of truth.
It remains to define precisely what we mean

by

"

fact,"

and what

is

the nature of the

correspondence which must subsist between
beUef and fact, in order that behef may be
true.

In accordance with our three requisites,
to seek a theory of truth which!

we have

allows truth to have an opposite, namely
falsehood, (2) makes truth a property of
(1)

makes

a property wholly
dependent upon the relation of the beliefs,

beliefs,

but

(3)

it

to outside things.

The necessity of allowing for falsehood
makes it impossible to regard belief as a
relation of the mind to a single object, which
could be said to be what is believed. If
belief were so regarded, we should find that,
like acquaintance, it would not admit of the
a

1

THE PROBLEMS OF PHILOSOPHY

194

opposition of truth and falsehood, but would
have to be always true. This may be made

by examples. Othello believes falsely
that Desdemona loves Cassio. We cannot
clear

say that this belief consists in a relation to a
"
single object,

Desdemona's love

for Cassio,"

if there were such an object, the belief
would be true. There is in fact no such
object, and therefore Othello cannot have
any relation to such an object. Hence his

for

belief

cannot possibly consist in a relation to

this object.

It

might be said that

"

to a different object,

mona

loves Cassio

difficult

his belief is a relation

namely

"
;

but

it

that Desde-

is

to suppose that there

almost as
is

such an

object as this, when Desdemona does not love
Cassio, as it was to suppose that there is

"

Desdemona's love

for

Cassio."

Hence

it

be better to seek for a theory of belief
which does not make it consist in a relation
will

mind

to a single object.
It is common to think of relations as though
they always held between two terms, but in
of the

fact this

is

not always the case.

Some

re-

TRUTH AND FALSEHOOD
lations

so
"

demand
Take,

on.

195

three terms, some four, and
for

instance,

the

relation

between." So long as only two terms
"
"
is imbetween
come in, the relation
possible

:

three terms are the smallest

that render

it

possible.

London and Edinburgh

;

number

between
York
but if London and
is

Edinburgh were the only places in the world,
there could be nothing which was between
one place and another.

Similarly jealousy

there can be no such
requires three people
three at least.
involve
not
does
relation that
"
Such a proposition as A wishes B to promote
" involves a relation of
C's marriage with D
:

four terms

;

that

D all come in, and

to say, A and B and C and
the relation involved cannot

is

be expressed otherwise than in a form inbe multivolving all four. Instances might

but enough has been said
plied indefinitely,
to show that there are relations which re-

two terms before they can
quire more than
occur.
The relation involved in judging or bemust, if falsehood is to be duly allowed
be taken to be a relation between several

lieving
for,

THE PROBLEMS OF PHILOSOPHY

196

between

not

terms,

two.

When

Othello

Desdemona loves Cassio, he
must not have before his mind a single object,
that

believes

"

Desdemona's love

Desdemona

loves

for

Cassio,"

Cassio,"

for

or

"

that

that would

require that there should be objective falsehoods, which subsist independently of any

minds

futable,

Thus

and

;

though not logically rea theory to be avoided if possible.
easier to account for falsehood if

is

it is

this,

we take judgment
mind and the

to be a relation in which

the

various objects concerned
that is to say, Desdemona
all occur severally
and loving and Cassio must all be terms in
;

the

relation

believes that

which subsists when Othello

Desdemona

relation, therefore,

since Othello also

is
is

loves Cassio.

This

a relation of four terms,
one of the terms of the

When we

relation.

four terms,

we

say that it is a relation of
do not mean that Othello has

a certain relation to Desdemona, and has the

same
This

relation to loving

and

also to Cassio.

be true of some other relation than

may

but believing, plainly, is not a
believing
relation which Othello has to each of the three
;

TRUTH AND FALSEHOOD

197

terms concerned, but to all of them together
there is only one example of the relation of
:

believing involved, but this one example
knits together four terms.
Thus the actual

moment when

occurrence, at the

entertaining his belief,
called "believing"

is

Othello

is

that the relation

knitting together into
one complex whole the four terms Othello,

Desdemona,

loving,

called belief or

is

and

judgment

Cassio.
is

What

is

nothing but this

relation of believing or judging,

which

relates

several things other than itself. An
act of belief or of judgment is the occurrence

a

mind to

between certain terms at some particular
time, of the relation of believing or judging.
are now in a position to understand

We

what it is that distinguishes a true judgment
from a false one. For this purpose we will
adopt certain

definitions.

In every act of

judgment there is a mind which judges, and
there are terms concerning which it judges.

We

will

call

judgment,
objects.

demona

the

mind the

subject in the

and the remaining terms the

Thus, when Othello judges that Desis the subject,

loves Cassio, Othello

THE PROBLEMS OF PHILOSOPHY

198

Desdemona and loving
The subject and the objects

while the objects are

and

Cassio.

together are called the constituents of the
judgment. It will be observed that the
of judging has what is called a
" or "
sense
direction."
We may say, meta-

relation

"

phorically, that
order,

it

puts

its

objects in a certain

which we may indicate by means

the order of the words in the sentence.

of

(In

an inflected language, the same thing will
be indicated by inflections, e.g. by the difference between nominative and accusative.)
Othello's

mona
mona

judgment that Cassio loves Desdefrom his judgment that Desde-

differs

loves Cassio, in spite of the fact that it
same constituents, because the

consists of the

relation of judging places the constituents
Simiin a different order in the two cases.

judges that Desdemona loves
Othello, the constituents of the judgment are

larly, if Cassio

the same, but their order is different.
This property of having a "sense" or "di"
rection
is one which the relation of judging
"
"
shares with all other relations. The
sense
still

of relations

is

the ultimate source of order

TRUTH AND FALSEHOOD
and

series

and a host

of

199

mathematical con-

but we need not concern ourselves

cepts
further with this aspect.
"
"
spoke of the relation called judging
" as
"
or
knitting together into one
believing
;

We

complex whole the subject and the
In this respect, judging

Whenever a
between two or more terms,
other relation.

terms into a complex
loves

Desdemona, there

whole as

"

objects,

is exactly like

it

whole.
is

every

relation holds

unites the
If

Othello

such a complex

Othello's love for

Desdemona."

The terms united by the relation may be
themselves complex, or may be simple, but
the whole which results from their being
united must be complex. Wherever there
is

a relation which relates certain terms, there

is

a complex object formed of the union
terms and conversely, wherever

of those

there

is

;

a complex object, there

which relates

its

constituents.

is

a relation

When an

act of believing occurs, there is a complex,
"
"
is the uniting
rein which
believing
are
and
and
lation,
objects
subject
arranged
in a certain order

by the "sense"

of the

i

THE PROBLEMS OF PHILOSOPHY

200

relation

of

Among

believing.

the objects,

we saw in considering " Othello believes
that Desdemona loves Cassio," one must be
as

a
"

relation

—in

this

But

the

instance,

this relation, as

it

relation

occurs in

loving."
the act of believing, is not the relation which
creates the unity of the complex whole conThe
sisting of the subject and the objects.
"
relation
as
it
occurs
in
the
act
of
loving,"
is
one
of
the
it
is
a brick
believing,
objects



in

the

cement

not

structure,
is

the belief

is

true,

the

cement.

"

the relation

believing."

there

is

The

When

another complex

unity, in which the relation which was one
of the objects of the belief relates the other
objects.

that

Thus,

e.g.,

Desdemona

if

Othello believes truly

loves Cassio, then there

is

a complex unity, " Desdemona's love for
Cassio," which is composed exclusively of
the objects of the belief, in the same order as
they had in the belief, with the relation which

was one of the objects occurring now as the
cement that binds together the other objects
of the belief.
belief

is false,

On

the other hand, when a
there is no such complex unity

TRUTH AND FALSEHOOD

of the objects of the oelief.

composed only

If Othello believes

falsely that

loves Cassio, then there

unity as

"

Thus a

201

is

no such complex

Desdemona's love

belief is true

Desdemona

when

for Cassio."

it

corresponds to

a certain associated complex, and false when
it does not.
Assuming, for the sake of definiteness, that the objects of the belief are

two terms and a

terms being put
"
" of the
sense
the
by
the two terms in that order

relation, the

in a certain order
believing, then

if

are united

by the

the belief

true

is

;

relation into a complex,
not, it

if

is

false.

constitutes the definition of truth

we were

and

This
false-

Judging or
believing is a certain complex unity of which
if the remaining
a mind is a constituent
constituents, taken in the order which they

hood that

in search of.

;

have in the

belief,

then the belief

is

form a complex unity,

true

;

if

not,

it is false.

Thus although truth and falsehood are
in a sense
properties of beliefs, yet they are
extrinsic properties, for the condition of the

something not involving
general) any mind at all, but

truth of a belief
beliefs, or (in

is

202

THE PROBLEMS OF PHILOSOPHY

only the objects of the

belief.

A

believes, believes truly

when

there

mind, which
is a corre-

sponding complex not involving the mind, but
only its objects. This correspondence ensures

and its absence entails
Hence we account simultaneously
truth,

'

falsehood.

two

for the

depend on minds for
do not depend on minds

facts that beliefs (o)
their existence, (6)

for their truth.

We may

restate our theory as follows

;

If

we take such a belief as " Othello believes
that Desdemona loves Cassio," we will call
Desdemona and Cassio the object-terms, and
loving the object-relation.

"
plex unity

If there is

Desdemona's love

a com-

for Cassio,"

consisting of the object-terms related by the
object-relation in the same order as they have

then this complex unity is called
the fact corresponding to the belief. Thus a
belief is true when there is a corresponding
fact, and is false when there is no correspondin the belief,

ing fact.
It will

be seen that minds do not

truth or falsehood.

when once

They

create

create beliefs, but

the beliefs are created, the

mind

TRUTH AND FALSEHOOD

203

cannot make them true or

false, except in the
concern
future things
special case where they
which are within the power of the person

catching trains. What
makes a belief true is a fact, and this fact does
believing,

such

as

not (except in exceptional cases) in any way
involve the mind of the person who has the
belief.

Having now decided what we mean by
truth and falsehood,

we have next

what ways there are

of

or that belief

is

to consider

knowing whether

true or false.

this

This considera-

tion will occupy the next chapter.

CHAPTER

XIII

KNOWLEDGE, ERROR, AND PROBABLE
OPINION

The

question as to what

we mean by truth

and falsehood, which we considered

in the

much less interest
preceding chapter,
than the question as to how we can know what
is

true and

what

of

This question will
occupy us in the present chapter. There can
be no doubt that some of our beliefs are

is

erroneous
certainty

is false.

thus we are led to inquire what
we can ever have that such and

;

such a belief is not erroneous.

In other words,

can we ever know anything at all, or do we
merely sometimes by good luck believe what
true ? Before we can attack this question,
we must, however, first decide what we mean
is

by

"

knowing," and this question
might be supposed.

easy as

204

is

not so

KNOWLEDGE AND ERROR
At

first

ledge

sight

we might imagine that know-

could be defined as

When what we

205

believe

is

"

true

true, it

belief.'*

might be

supposed that we had achieved a knowledge
But this would not acof what we believe.
cord with the

in

way
To
used.
commonly
stance

If

:

a

man

which the word

is

take a very trivial inthat the late

believes

Prime Minister's last name began with a B, he
believes what is true, since the late Prime
Minister was Sir Henry Campbell Bannerman.

But

if

he believes that Mr. Balfour was the

Prime Minister, he will still believe that
Prime Minister's last name began
with a B, yet this belief, though true, would

late

the late

If

not be thought to constitute knowledge.

a

newspaper, by an intelligent anticipation,
announces the result of a battle before any
telegram giving the result has been received, it
may by good fortune announce what after-

wards turns out to be the right result, and it
may produce belief in some of its less experienced readers.

But

in spite of the truth of

their belief, they cannot be said to
ledge.

Thus it is

have know-

clear that a true belief

is

not

THE PROBLEMS OF PHILOSOPHY

206

knowledge when

it

is

deduced from a

false

belief.

In like manner, a true belief cannot be
knowledge when it is deduced by a

called

fallacious process of reasoning,

even

if

the

premisses from which it is deduced are true.
If I know that all Greeks are men and that
Socrates was a man, and I infer that Socrates
was a Greek, I cannot be said to know that
Socrates was a Greek, because, although my
premisses and my conclusion are true, the
conclusion does not follow from the premisses.

But are we to say that nothing is knowledge
except what is validly deduced from true
premisses ? Obviously we cannot say this.
Such a definition is at once too wide and too
In the

narrow.

because

it is

should be

man who
late

first

place,

it

is

too wide,

not enough that our premisses
they must also be known. The

true,

was the
Prime Minister may proceed to draw
believes that Mr. Balfour

valid deductions from the true premiss that the
late

Prime Minister's name began with a B,

but he cannot be said to know the conclusions
reached by these deductions.

Thus we

shall

KNOWLEDGE AND ERROR

207

have to amend our definition by saying that
knowledge is what is vaHdly deduced from

known premisses.
cular definition

know what

is

:

This, however,
it

is

a

cir-

assumes that we already

meant by " known premisses."

It can, therefore, at best define

knowledge, the sort

we

call

one sort of

derivative, as

opposed to intuitive knowledge.
"
Derivative knowledge is what
say
:

We may
is

validly

deduced from premisses known intuitively."
In this statement there is no formal defect,
but

it

ledge

leaves the definition of intuitive
still

know-

to seek.

Leaving on one

side, for the

moment, the

question of intuitive knowledge, let us consider the

above suggested definition of de-

rivative knowledge.
it

is

that

it

The

chief objection to

unduly limits knowledge.

It

constantly happens that people entertain a
true belief, which has grown up in them because of some piece of intuitive knowledge from

which it is capable of being validly inferred,
but from which it has not, as a matter of fact,
been inferred by any logical process.
Take, for example, the beliefs produced by

208

THE PROBLEMS OF PHILOSOPHY

If the newspapers announce the
death of the King, we are fairly well justified

reading.

in believing that the
is

be

King is dead, since this
the sort of announcement which would not

made

were

And we

are quite
amply justified in believing that the newspaper asserts that the King is dead. But here
if it

false.

the intuitive knowledge upon which our belief
is based is knowledge of the existence of sense-

data derived from looking at the print which
gives the news. This knowledge scarcely
except in a person
read easily. A child may be
aware of the shapes of the letters, and pass
rises into consciousness,

who cannot

gradually and painfully to a realisation of
their meaning.

But anybody accustomed to
what the letters

reading passes at once to

not av/are, except on reflection,
that he has derived this knowledge from the

mean, and

is

sense-data called seeing the printed letters.
Thus although a valid inference from the

meaning is possible, and could
be performed by the reader, it is not in fact
letters to their

performed, since he does not in fact perform
any operation which can be called logical

KNOWLEDGE AND ERROR
Yet

inference.

it

200

would be absurd to

say-

that the reader does not know that the news-

paper announces the King's death.
We must, therefore, admit as derivative
knowledge whatever is the result of intuitive

knowledge even

if

by mere

association, pro-

a valid logical connection, and
the person in question could become aware of
this connection by reflection.
There are in

vided there

is

ways, besides logical inference, by
which we pass from one belief to another the
fact

many

:

passage from the print to its meaning illustrates these ways.
These ways may be called
"

psychological inference." We shall, then,
admit such psychological inference as a means
of obtaining derivative

there

is

knowledge, provided
a discoverable logical inference which

runs parallel to the psychological inference.
This renders our definition of derivative knowledge less precise than we could wish, since
"
"
the word
discoverable
is vague
it does
:

not

tell

us

how much reflection may be needed
make the discovery. But in fact

in order to

"

"

knowledge
merges into

"

is

not a precise conception

probable opinion," as

we

:

it

shall

THE PROBLEMS OF PHILOSOPHY

210
see

more

chapter.

fully in the course of the present

A very

precise definition, therefore,

should not be sought, since any such definition
must be more or less misleading.
The chief difficulty in regard to knowledge,
however, does not arise over derivative knowSo long
ledge, but over intuitive knowledge.
as we are dealing with derivative knowledge,
we have the test of intuitive knowledge to fall
back upon. But in regard to intuitive beliefs,
it is by no means easy to discover any criterion
by which to distinguish some as true and

In this question it is
scarcely possible to reach any very precise
result
all our knowledge of truths is infected
others as erroneous.

:

with some degree of doubt, and a theory which
ignored this fact would be plainly wrong.

Something

be done, however, to mitigate
of the question.

may

the difficulties

Our theory

of truth, to begin with, supplies

the possibility of distinguishing certain truths
as self-evident in a sense which ensures infallibility.

When

a

belief is true,

we

said,

a corresponding fact, in which the
several objects of the belief form a single
there

is

KNOWLEDGE AND ERROR
The

complex.

belief

is

said

knowledge of this fact, provided

211

to constitute
it fulfils

those

further somewhat vague conditions which we
have been considering in the present chapter.

any fact, besides the knowledge constituted by belief, we may also have
the kind of knowledge constituted by perception (taking this word in its widest possible
But

in regard to

For example, if you know the hour
the sunset, you can at that hour know the

sense).

of

fact that the sun
of the fact

is

setting

by way

:

this

is

knowledge

of

knowledge of truths
the weather is fine, look
;

but you can also, if
to the west and actually see the setting sun
you then know the same fact by the way of
:

knowledge of things.
Thus in regard to any complex fact, there
are, theoretically, two ways in which it may
be known

which

its

:

by means

a judgment, in
several parts are judged to be
(1)

of

related as they are in fact related

means
itself,

of acquaintance with the

which

may

(in

;

(2)

complex

by
fact

a large sense) be called
by no means confined

it is

perception, though
to objects of the senses.

Now

it

will

be

212

THE PROBLEMS OF PHILOSOPHY

observed that the second

complex

fact,

the

when

of

way

knowing a

way of acquaintance, is
there really is such a fact,

only possible
while the first way, like all judgment, is
The second way gives us
liable to error.
the complex whole, and

when

therefore only

is

parts do actually have that
possible
relation which makes them combine to form
such a complex. The first way, on the contrary, gives us the parts and the relation
severally, and demands only the reality of
its

the relation may
the parts and the relation
not relate those parts in that way, and yet
the judgment may occur.
:

It will be

remembered that

XI we

at the

end

of

suggested that there might

Chapter
be two kinds of self-evidence, one giving an

absolute guarantee of truth, the other only a
These two kinds can now
partial guarantee.

be distinguished.
We may say that a truth
in the first

is

and most absolute

self-evident,

sense,

when

we have acquaintance with the fact which
corresponds to the truth. When Othello
believes that

Desdemona

loves Cassio, the

KNOWLEDGE AND ERROR

218

corresponding fact, if his belief were true,
"
would be
Desdemona's love for Cassio."
This would be a fact with which no one could

have acquaintance except Desdemona
in the sense of self-evidence that
sidering,

we

;

hence

are con-

the truth that Desdemona loves

were a truth) could only be selfevident to Desdemona. All mental facts,
Cassio

(if it

and all facts concerning sense-data, have this
same privacy
there is only one person to
:

whom

they can be self-evident in our present
sense, since there is only one person who can
be acquainted with the mental things or the
sense-data concerned.

Thus no

fact about

any particular existing thing can be selfevident to more than one person. On the
other hand, facts about universals do not
privacy. Many minds may be
acquainted with the same universals ; hence
a relation between universals may be known

have

this

In

all

cases

to

many different people.
where we know by acquaintance

by acquaintance

a complex fact consisting of certain terms in
a certain relation, we say that the truth that
these terms are so related has the

first

or

214

THE PROBLEMS OF PHILOSOPHY

absolute kind of self-evidence, and in these

judgment that the terms are so
related must be true. Thus this sort of selfevidence is an absolute guarantee of truth.
But although this sort of self-evidence is an
cases the

absolute guarantee of truth, it does not enable
us to be absolutely certain, in the case of any

given judgment, that the judgment in question is true.
Suppose we first perceive the

sun shining, which is a complex fact, and
"
the
thence proceed to make the judgment
sun is shining." In passing from the perception to the judgment, it is necessary to

we have to
analyse the given complex fact
"
"
"
"
sun
as
out
the
and
shining
separate
constituents of the fact. In this process it
:

is

possible to

where a

fact

commit an

has the

first

error

;

hence even

or absolute kind of

self-evidence, a judgment believed to correspond to the fact is not absolutely infallible,

because
fact.

it

may

But

if it

not really correspond to the
does correspond (in the sense

explained in the preceding chapter),

must be

then

it

true.

The second

sort of self -evidence will be that

KNOWLEDGE AND ERROR

215

which belongs to judgments in the first
instance, and is not derived from direct
perception of a fact as a single complex
whole. This second kind of self-evidence

have degrees, from the very highest
degree down to a bare inclination in favour

will

Take, for example, the case of
a horse trotting away from us along a hard
road. At first our certainty that we hear the
of the belief.

hoofs

is

intently,

we listen
comes a moment when we

complete
there

;

gradually,

if

think perhaps it was imagination or the blind
at last we
upstairs or our own heart-beats
;

become doubtful whether there was any noise
then we think we no longer hear
at all
anything, and at last we know we no longer
;

hear anything. In this process, there is a
continual gradation of self-evidence, from the
highest degree to the least, not in the sensedata themselves, but in the judgments based

on them.

Or again: Suppose we are comparing two
shades of colour, one blue and one green.

We can be quite sure they are different shades
of colour

;

but

if

the green colour

is

gradually

216

THE PROBLEMS OF PHILOSOPHY

altered to be

more and more

like the blue,

a blue-green, then a greenybecoming
blue, then blue, there will come a moment
first

when we

we can see any
difference, and then a moment when we
know that we cannot see any difference.
The same thing happens in tuning a musical
are doubtful whether

instrument, or in any other case where there
is a continuous gradation.
Thus self-evidence
of this sort is a

matter of degree

;

and

it

seems plain that the higher degrees are more
to be trusted than the lower degrees.

knowledge our ultimate
premisses must have some degree of selfIn

derivative

evidence, and so

must

their connection with

the conclusions deduced from them.

Take for

example a piece of reasoning in geometry.
It is not enough that the axioms from which

we start should be self-evident

it is necessary
the
also that, at each step in
reasoning, the
connection of premiss and conclusion should

In

be self-evident.

:

difficult reasoning,

this

connection has often only a very small degree

hence errors of reasoning are
not improbable where the difficulty is great.
of self -evidence

;

KNOWLEDGE AND ERROR
From what has been

said

it is

217

evident that,

both as regards intuitive knowledge and as
regards derivative knowledge, if we assume
that intuitive knowledge is trustworthy in
proportion to the degree of its self-evidence,
there will be a gradation in trustworthiness,
from the existence of noteworthy sense-data

and the simpler truths of logic and arithmetic, which may be taken as quite certain,
down to judgments which seem only just
more probable than their opposites. What

we

firmly believe,

provided

ledge,
f erred

logically.

true,

is

if it is

it

(logically

intuitive

if it is

is

or

true, is called

either intuitive or

psychologically)

knowledge from which

What we

called error.

know-

firmly believe,

What we

it

in-|

from]

is

'

follows

if it is

not]
firmly believe,
'

neither knowledge nor error, and also
believe hesitatingly, because it is,

what we
or

1

derived from, something which has not
may be

the highest degree of self -evidence,
called probable opinion.
Thus the

greater

what would commonly pass as knowledge is more or less probable opinion.
part of

In regard to probable opinion,

we can

218

THE PROBLEMS OF PHILOSOPHY

derive great assistance from coherence, which
we rejected as the definition of truth, but may

A

often use as a criterion.
ally

if

probable opinions,

body

of individu-

they are mutually

become more probable than any one
them would be individually. It is in this

coherent,
of

way that many

scientific

hypotheses acquire
into a coherent
They
and
thus become
system of probable opinions,
more probable than they would be in isolatheir probability.

tion.

fit

The same thing

applies

to

general

philosophical hypotheses. Often in a single
case such hypotheses may seem highly doubtful, while yet, when we consider the order

and coherence which they introduce into a
mass of probable opinion, they become pretty
nearly certain. This applies, in particular,
to such matters as the distinction between

dreams and waking life. If our dreams, night
after night, were as coherent one with another
as our days, we should hardly know whether
to believe the dreams or the waking

life.

As it is, the test of coherence condemns the
dreams and confirms the waking life. But
this

test,

though

it

increases

probability

I

KNOWLEDGE AND ERROR
wnere

it

is

successful,

219

never gives absolute

certainty, unless there is certainty already
Thus
at some point in the coherent system.

the mere organisation of probable opinion
will

never,

by

itself,

dubitable knowledge.

transform

it

into in-

CHAPTER XIV
THE LIMITS OF PHILOSOPHICAL KNOWLEDGE

we have said hitherto concerning
we
have scarcely touched on many
philosophy,
In

all

that

matters that occupy a great space in the

most philosophers. Most philoor, at any rate, very many
profess
to be able to prove, by a priori metaphysical
writings of


sophers



reasoning, such things as the fundamental
dogmas of religion, the essential rationality
of the universe, the illusoriness of matter, the

unreality of all evil, and so on. There can be
no doubt that the hope of finding reason to
believe such theses as these has been the
chief inspiration of many life-long students
of philosophy.
This hope, I believe, is vain.
It would seem that knowledge concerning the

universe as a whole

not to be obtained by
metaphysics, and that the proposed proofs
that, in virtue of the laws of logic, such and
is

220

THE LIMITS OF KNOWLEDGE

2J1

such things must exist and such and such
others cannot, are not capable of surviving a
critical

In this chapter we shall

scrutiny.

briefly consider the kind of

such reasoning

is

way

in

which

attempted, with a view
we can hope that it

to discovering whether

may

be valid.

The great representative, in modern times,
of the kind of view which we wish to examine,
was Hegel (1770-1831). Hegel's philosophy
very difficult, and commentators differ

is

the true interpretation of it.
According to the interpretation I shall adopt,
which is that of many, if not most of the
as to

commentators, and has the merit of giving
an interesting and important type of philosophy, his main thesis is that everything
short of the

Whole

is

obviously fragmentary,

and obviously incapable of existing without
the complement supplied by the rest of the
world. Just as a comparative anatomist, from
a single bone, sees what kind of animal the
whole must have been, so the metaphysician,
according to Hegel, sees, from any one piece
of reality, what the whole of reality must be



THE PROBLEMS OF PHILOSOPHY

222

at least in

its

outlines.

Every apparently separate piece of reality has, as it
were, hooks which grapple it to the next piece
large

;

the next piece, in turn, has fresh hooks, and so
on, until the whole universe is reconstructed.

This essential incompleteness appears, according to Hegel, equally in the world of thought

and

world of things. In the world of
we take any idea which is abstract

in the

thought,

if

or incomplete,
if

we

we

its

on examination, that,
incompleteness, we become
find,

forget
in contradictions

involved

these

;

contra-

dictions turn the idea in question into its
opposite, or antithesis ; and in order to escape,

we have
which

is

to find a new, less incomplete idea,
the synthesis of our original idea and

its antithesis.

This

new
we

the idea

idea,

though

less

incomplete than

started with, will be found, never-

theless, to be

still

not wholly complete, but to
it must be

pass into its antithesis, with which

combined

in a

new

synthesis.

In this

Hegel advances until he reaches the

"

waj'^

Absolute

Idea," which, according to him, has no incompleteness, no opposite, and no need of

THE LIMITS OF KNOWLEDGE
further

;

reality as
it

is

but
it

to one

Whole.

Idea,

adequate to describe Absolute

is

therefore,

Reality

The Absolute

development.

223

lower ideas only describe
appears to a partial view, not as
all

who

simultaneously surveys the

Thus Hegel reaches the conclusion

that Absolute Reality forms one single harmonious system, not in space or time, not in

any degree
spiritual.

the world

evil,

wholly rational, and wholly

Any appearance to

the contrary, in

we know, can be proved

so he believes

—to

logically



be entirely due to our
fragmentary piecemeal view of the universe.

we saw the universe whole, as we may
suppose God sees it, space and time and matter
If

and

and all striving and struggling would
disappear, and we should see instead an eternal
evil

]

perfect unchanging spiritual unity.

\

In this conception, there is undeniably something sublime, something to which we could
wish to yield assent.

Nevertheless,

when the

arguments in support of it are carefully
examined, they appear to involve much confusion and many unwarrantable assumptions.

The fundamental tenet upon which the system

224

THE PROBLEMS OF PHILOSOPHY

built up is that what is incomplete must be
not self-subsistent, but must need the support
of other things before it can exist.
It is held
is

that whatever has relations to things outside
itself must contain some reference to those

outside things in
not, therefore,

own

its

be what

things did not exist.
example, is constituted

nature,

it is if

and could

those outside

A

man's nature, for
by his memories and

the rest of his knowledge, by his loves and
hatreds, and so on thus, but for the objects
;

which he knows or loves or hates, he could
not be what he is. He is essentially and
obviously a fragment
of reality he

:

taken as the sum-total

would be self-contradictory.

This whole point of view, however, turns
"
"
upon the notion of the nature of a thing,

which seems to mean

"'

all

the truths about

the thing." It is of course the case that a
truth which connects one thing with another
thing could not subsist if the other thing
did not subsist.

But a truth about a thing

not part of the thing itself, although it
must, according to the above usage, be part
"
"
If we mean
of the thing.
of the
nature

is

THE LIMITS OF KNOWLEDGE
"
"
by a thing's nature

all

225

the truths about the

we cannot know a thing's
we know all the thing's re-

thing, then plainly

"

nature

"

unless

lations to all the other things in the universe.

But

if

the word

"

nature

"

is

used in this

we shall have to hold that the thing
known when its " nature " is not
may
known, or at any rate is not known completely.
There is a confusion, when this use of the
word " nature " is employed, between knowsense,

be

ledge of things and knowledge of truths.

We

may have knowledge of a thing by acquaintance even if we know very few propositions
about it theoretically we need not know any



propositions about it. Thus, acquaintance
with a thing does not involve knowledge of its
"
"
nature
in the above sense.
And although

acquaintance with a thing is involved in our
knowing any one proposition about a thing,

knowledge
is

of its

"

nature," in the above sense,

not involved.

Hence, ( 1 ) acquaintance with
a thing does not logically involve a knowledge
of its relations, and (2) a knowledge of some of
its

relations does not involve a

of all of its relations nor a

knowledge
knowledge of its

226
"

THE PROBLEMS OF PHILOSOPHY

nature

"

in the

above sense.

quainted, for example, with

and

I

my

may

be ac-

toothache,

knowledge may be as complete as
knowledge by acquaintance ever can be, withthis

out knowing all that the dentist (who is not
acquainted with it) can tell me about its
cause,

"

and without therefore knowing its
"
in the above sense.
Thus the fact

nature

that a thing has relations does not prove that
are logically necessary. That is
to say, from the mere fact that it is the thing
its relations

it is

we cannot deduce that

it

must have the

various relations which in fact

it

has.

only seems to follow because we
already.
It follows that

This

know

it

we cannot prove that the

universe as a whole forms a single harmonious
system such as Hegel believes that it forms.

And

if

we cannot prove

this,

we

also cannot

prove the unreality of space and time and
matter and evil, for this is deduced by Hegel

from the fragmentary and relational character
Thus we are left to the
of these things.
piecemeal investigation of the world, and are
unable to know the characters of those parts

THE LIMITS OF KNOWLEDGE
of the universe that are

perience.

227

remote from our ex-

This result, disappointing as

it is

to those whose hopes have been raised by the
systems of philosophers, is in harmony with
the inductive and scientific temper of our age,
and is borne out by the whole examination
of

human knowledge which

has occupied our

previous chapters.
Most of the great ambitious attempts of
metaphysicians have proceeded by the at-

tempt to prove that such and such apparent
features of the actual world were self-contra-

and therefore could not be real. The
whole tendency of modern thought, however,
is more and more in the direction of showing
dictory,

that the supposed contradictions were illusory,
and that very little can be proved a priori

from considerations of what must

be.

A good

by space and
time
and
appear to be infinite
Space
If we
extent, and infinitely divisible.

illustration of this is afforded

time.
in

travel along a straight line in either direction,
it is difficult to believe that we shall finally

reach a last point, beyond which there
nothing, not even empty space. Similarly,

is
if

1

228

THE PROBLEMS OF PHILOSOPHY

in imagination we travel backwards or forwards in time, it is difficult to believe that we
shall reach

a

first

or last time, with not even

it.
Thus space
to
infinite
in
be
extent.
appear

empty time beyond
if

Again,
it

we take any two

and time

points on a line,

seems evident that there must be other

points between them, however small the distance between them may be
every distance
:

can be halved, and the halves can be halved
In time,
again, and so on ad infinitum.

however little time may elapse
between two moments, it seems evident that
there will be other moments between them.
Thus space and time appear to be infinitely
But as against these apparent facts
divisible.
infinite extent and infiiiite divisibility
philosophers have advanced arguments tending to show that there could be no infinite
similarly,





collections of things,

number
must be

and that therefore the

of points in space, or of instants in

time,

finite.

Thus a contradiction

emerged between the apparent nature of space
and time and the supposed impossibility of
infinite collections.

THE LIMITS OF KNOWLEDGE

229

Kant, who first emphasised this contradiction, deduced the impossibihty of space and
time, which he declared to be merely sub-

and since his time very many philotime
sophers have believed that space and
are mere appearance, not characteristic of the
jective

;

world as

it

really

is.

Now, however, owing

to the labours of the mathematicians, notably

Georg Cantor,

it

has appeared that the imposwas a mistake.

sibility of infinite collections

They are not

in fact self-contradictory, but

only contradictory of certain rather obstinate
mental prejudices. Hence the reasons for
regarding space and time as unreal have become inoperative, and one of the great sources
of metaphysical constructions

is

dried up.

The mathematicians, however, have not
been content with showing that space as it is
commonly supposed to be is possible they
have shown also that many other forms of
;

space are equally possible, so far as logic can
show. Some of Euclid's axioms, which appear
to

common

sense to be necessary, and were

formerly supposed to be necessary by philosophers, are

now known to derive their appear-

230

THE PROBLEMS OF PHILOSOPHY

ance of necessity from our mere familiarity

with actual space, and not from any a priori
By imagining worlds in
logical foundation.

which these axioms are

false,

the mathemati-

cians have used logic to loosen the prejudices
of common sense, and to show the possibility
of spaces differing

from that

in

— some

which we

live.

more, some

less



And some of these

spaces differ so little from Euclidean space,
where distances such as we can measure are

concerned, that

impossible to discover by
observation whether our actual space is strictly
it is

Euclidean or of one of these other kinds.

Thus the position

completely reversed.
that
Formerly
experience left
appeared
only one kind of space to logic, and logic
showed this one kind to be impossible. Now,
is

it

logic presents

many

kinds of space as possible

apart from experience, and experience only
Thus, while
partially decides between them.

our knowledge of what

is has become less than
was formerly supposed to be, our knowledge
of what may be is enormously increased.
In-

it

stead of being shut in within narrow walls,
of which every nook and cranny could be

THE LIMITS OF KNOWLEDGE

281

in an open
where much remains
unknown because there is so much to know.
What has happened in the case of space and

explored,

we

find

ourselves

world of free possibilities,

time has happened, to some extent, in other

The attempt to prescribe
the universe by means of a priori principles

directions as well.

to

has broken

down

;

logic, instead of being, as

formerly, the bar to possibilities, has become
the great liberator of the imagination, presenting innumerable alternatives which are closed

common

and leaving to
experience the task of deciding, where decision
is possible, between the many worlds which
to unrefiective

sense,

Thus knowledge as
to what exists becomes limited to what v/e can
learn from experience not to what we can
actually experience, for, as we have seen, there

logic offers for

our choice.



much knowledge by description concerning
things of which we have no direct experience.

is

But in all cases of knowledge by description,
we need some connection of universals, enabling us,

from such and such a datum, to

infer

an object of a certain sort as implied by our
datum. Thus in regard to physical objects,

232

THE PROBLEMS OF PHILOSOPHY

for example, the principle that sense-data are

signs of physical objects
of universals

;

and

is itself

a connection

only in virtue of this

it is

principle that experience enables us to acquire

knowledge concerning physical objects. The
same applies to the law of causality, or, to
descend to what

is less

general, to such prin-

law of gravitation.
Principles such as the law of gravitation

ciples as the

are proved,

or rather are rendered highly

probable, by a combination of experience with
some wholly a priori principle, such as the
principle of induction.

knowledge, which

knowledge

is

Thus our

the source of

of truths,

is

of

two

all

intuitive

our other

sorts

;

pure

empirical knowledge, which tells us of the
existence and some of the properties of particular things with which

we

are acquainted,
and pure a priori knowledge, which gives us
connections between universals, and enables

us to draw inferences from the particular
facts given in empirical knowledge.

Our

deri-

vative knowledge always depends upon some

pure a priori knowledge and usually also de-

pends upon some pure empirical knowledge.

THE LIMITS OF KNOWLEDGE
Philosophical knowledge,

above

said

is

if

233

what has been

true, does not differ essentially

knowledge there is no special
source of wisdom which is open to philosophy
but not to science, and the results obtained by
philosophy are not radically different from
from

scientific

;

The essential
philosophy, which makes it a

those obtained from science.
characteristic of

study distinct from science, is criticism. It
examines critically the principles employed in
science

and in daily life

consistencies there

and

it

;

may

it

searches out any in-

be in these principles,

only accepts them when,

as the result of

a critical inquiry, no reason for rejecting them
has appeared. If, as many philosophers have
believed, the principles underlying the sciences

were capable, when disengaged from irrelevant
us knowledge concerning the
universe as a whole, such knowledge would

detail, of giving

have the same claim on our

belief as scientific

but our inquiry has not reknowledge has
vealed any such knowledge, and therefore, as
;

regards the special doctrines of the bolder
metaphysicians, has had a mainly negative
result.
But as regards what would be com-

234

THE PROBLEMS OF PHILOSOPHY

monly accepted as knowledge, our result is in
we have seldom found
the main positive
:

reason to reject such knowledge as the result
of our criticism, and we have seen no reason

man

incapable of the kind of
knowledge which he is generally believed
to possess.

to suppose

When, however, we speak
a criticism of knowledge, it
pose a certain limitation.

is

of philosophy as

necessary to imwe adopt the

If

attitude of the complete sceptic, placing ourselves wholly outside all knowledge, and
asking,

from

this

compelled

outside

position,

return within the

to

to be

circle

of

knowledge, we are demanding what is impossible, and our scepticism can never be
refuted.

For

some piece
tants share

all

refutation

must begin with

knowledge which the dispufrom blank doubt, no argument

of
;

can begin. Hence the criticism of knowledge
which philosophy employs must not be of
this destructive kind, if any result is to be
Against this absolute scepticism,
no logical argument can be advanced. But it
is not difficult to see that scepticism of this
achieved.

THE LIMITS OF KNOWLEDGE
kind

unreasonable.

is

cal doubt,"
is

Descartes'

"

235

methodi-

with which modern philosophy

not of this kind, but

began,
kind of criticism which

is

rather the

we are asserting to be
"
methodical
the essence of philosophy. His
"
consisted in doubting whatever
doubt
seemed doubtful

;

in pausing, with each ap-

parent piece of knowledge, to ask himself
whether, on reflection, he could feel certain
that he really knew it. This is the kind of
criticism

which constitutes philosophy.

Some

knowledge, such as knowledge of the existence
of our sense-data, appears quite indubitable,

however calmly and thoroughly we

upon

it.

reflect

In regard to such knowledge, philo-

sophical criticism does not require that we
should abstain from belief. But there are
beliefs

— such,

for example, as the belief that

physical objects exactly resemble our sensedata which are entertained until we begin



to reflect, but are found to melt

away when

subjected to a close inquiry. Such beliefs
philosophy will bid us reject, unless some

new

line of

them.

But

argument

is

found to support

to reject the beliefs which do not

236

THE PROBLEMS OF PHILOSOPHY

any objections, however
closely we examine them, is not reasonable,
and is not what philosophy advocates.
The criticism aimed at, in a word, is not
appear open

to

that which, without reason, determines to re-

but that which considers each piece of
apparent knowledge on its merits, and retains
ject,

whatever

still

appears to be knowledge when

this consideration is completed.
risk of error

That some

remains must be admitted, since

human beings are fallible. Philosophy may
claim justly that it diminishes the risk of error,
and that in some cases it renders the risk so
small as to be practically negligible. To do
more than this is not possible in a world where
and more than this no
mistakes must occur
;

prudent advocate of philosophy would claim
to have performed.

CHAPTER XV
THE VALUE OF PHILOSOPHY

Having now come

to the end of our brief

and very incomplete review
of philosophy,

of the problems
be well to consider, in
the value of philosophy

it will

what is
and why it ought to be studied. It is the
more necessary to consider this question, in
view of the fact that many men, under the
conclusion,

influence of science or of practical affairs, are
inclined to doubt whether philosophy

thing better than innocent but useless

is

any-

trifling,

hair-splittingdistinctions, and controversies on
matters concerning which knowledge is impossible.

This view of philosophy appears to result,
partly from a wrong conception of the ends
of

life,

partly from a

wrong conception

of

the kind of goods which philosophy strives to
237

288

THE PROBLEMS 01 PHILOSOPHY
Physical science, through the me-

achieve.

dium

innumerable

of inventions, is useful to

thus
people who are wholly ignorant of it
the study of physical science is to be recommended, not only, or primarily, because of the
;

on the student, but rather because of
the effect on mankind in general. This utility
effect

does not belong to philosophy.
of philosophy has any value at

than students of philosophy,
indirectly,
of those

through

who study

therefore,

if

its effects
it.

anywhere,

It

is

If
all

the study
for others

must be only
upon the lives

it

in these effects,

that the value of

philosophy must be primarily sought.
But further, if we are not to fail in our en-

deavour to determine the value of philosophy,
we must first free our minds from the pre-

what are wrongly called
The " practical " man, as

judices of

men.

often used,
needs,

who

is

"

"
practical

this

word

is

one who recognises only material
men must have food

realises that

for the body, but

is

oblivious of the necessity

If all men
of providing food for the mind.
were well off, if poverty and disease had been

reduced to their lowest possible point, there

THE VALUE OF PHILOSOPHY

239

would still remain much to be done to produce
a valuable society and even in the existing
world the goods of the mind are at least as
;

important as the goods of the body. It is
exclusively among the goods of the mind that
the value of philosophy is to be found
and
those
who
are
not
indifferent
to
these
only
;

goods can be persuaded that the study of
philosophy is not a waste of time.
Philosophy, like all other studies, aims
primarily at knowledge. The knowledge it
is the kind of knowledge which gives
and
unity
system to the body of the sciences,
and the kind which results from a critical

aims at

examination of the grounds of our convictions,
But it cannot be
prejudices, and beliefs.
maintained that philosophy has had any very
great measure of success in its attempts to
provide definite answers to its questions. If
you ask a mathematician, a mineralogist, a

any other man of learning, what
body of truths has been ascertained

historian, or
definite

by his science, his answer will last as long as
you are willing to listen. But if you put the
same question to a philosopher, he will, if he is

240

THE PROBLEMS OF PHILOSOPHY

candid, have to confess that his study has not
achieved positive results such as have been

achieved by other sciences. It is true that
this is partly accounted for by the fact that,
as soon as definite knowledge concerning any
subject becomes possible, this subject ceases
to be called philosophy, and becomes a sepaThe whole study of the heavens,
rate science.

which now belongs to astronomy, was once
Newton's great work
included in philosophy
;

"

the mathematical principles of
natural philosophy." Similarly, the study of

was called
the

human mind, which

was, until very lately,

a part of philosophy, has

now been

separated

from philosophy and has become the science
of psychology.

Thus, to a great extent, the

uncertainty of philosophy is more apparent
those questions which are already
than real
:

capable of definite answers are placed in the
sciences, while those only to which, at present,
no definite answer can be given, remain to

form the residue which

is

called philosophy.

however, only a part of the truth
concerning the uncertainty of philosophy.
This

is,

There are

many

questions

—and among them

THE VALUE OF PHILOSOPHY
those that are of
to our spiritual

can

see,

must

241

the profoundest interest

life

— which,

so far

remain insoluble to the

as we
human

powers become of quite a
Has
different order from what they are now.

intellect unless its

the universe any unity of plan or purpose, or
Is
is it a fortuitous concourse of atoms ?
consciousness a permanent part of the unigiving hope of indefinite growth in
wisdom, or is it a transitory accident on a
verse,

must ultimately
Are good and evil of

small planet on which

become impossible

?

life

importance to the universe or only to man ?
Such questions are asked by philosophy, and
variously answered by various philosophers.

But

it

would seem

that,

whether answers be

otherwise discoverable or not, the answers
of them
suggested by philosophy are none

demonstrably true. Yet, however slight
be the hope of discovering an answer,

may
it

is

to continue
part of the business of philosophy
such
of
consideration
the
questions, to make us
aware of their importance, to examine all the

approaches to them, and to keep alive that
which is
speculative interest in the universe

242

THE PROBLEMS OF PHILOSOPHY

apt to be killed by confining ourselves to
definitely ascertainable knowledge.

Many philosophers,

it is

true,

have held that

philosophy could establish the truth of certain

answers to such fundamental questions. They
have supposed that what is of most importance
in religious beliefs could be proved

by

strict

demonstration to be true.
of such attempts,

is

it

In order to judge
necessary to take a

human knowledge, and

to form an
methods and its limitations.
On such a subject it would be unwise to

survey of

opinion as to its

but if the investipronounce dogmatically
gations of our previous chapters have not led
us astray, we shall be compelled to renounce
;

the hope of finding philosophical proofs of
religious beliefs.

We

cannot, therefore, in-

clude as part of the value of philosophy any
set of answers to such questions.

definite

Hence, once more, the value of philosophy
must not depend upon any supposed body of
definitely ascertainable

knowledge to be ac-

quired by those who study it.
The value of philosophy is, in fact, to be

sought largely in

its

very uncertainty.

The

THE VALUE OF PHILOSOPHY

243

man who

has no tincture of philosophy goes
Hfe
imprisoned in the prejudices dethrough
rived from common sense, from the habitual
beliefs of

his age

or his nation, and from

convictions which have grown up in

his

mind

/

without the co-operation or consent of hisj
To such a man the world

deliberate reason.

tends to become definite, finite, obvious
common objects rouse no questions, and un;

familiar possibilities are contemptuously reAs soon as we begin to philosophise,
jected.

on the contrary, we

find, as

we saw

in our

opening chapters, that even the most everyday things lead to problems to which only
very incomplete answers can be given. Philosophy, though unable to tell us with certainty
is the true answer to the doubts which

what

it raises, is

able to suggest

many

possibilities

which enlarge our thoughts and free them
from the tyranny of custom. Thus, while
diminishing our feeling of certainty as to what
things are, it greatly increases our knowledge

what they may be it removes the somewhat arrogant dogmatism of those who have
as to

;

never travelled into the region of liberating

2i4

THE PROBLEMS OF PHILOSOPHY

doubt, and

by

it

keeps alive our sense of wonder

showing familiar things in an unfamiliar

aspect.

Apart from
pected

utility in

its

showing unsus-



philosophy has a value
chief value
through the greatness

possibilities,

perhaps its
of the objects which



contemplates, and the

it

freedom from narrow and personal aims reThe life of
sulting from this contemplation.
the instinctive
circle of

friends

his

may

man

is

shut up within the

family and
be included, but the outer world
interests

private

not regarded except as
what comes within the
is

wishes.

In such a

feverish

and confined,

life

which the philosophic

The private world

it

:

may help or hinder

circle of instinctive

there
in

life

is

something
comparison with
is calm and free.

of instinctive interests

is

a

small one, set in the midst of a great and powerworld which must, sooner or later, lay our

ful

private world in ruins. Unless we can so
enlarge our interests as to include the whole

outer world,

we remain

like a garrison in a

beleaguered fortress, knowing that the enemy
prevents escape and that ultimate surrender

THE VALUE OF PHILOSOPHY
is

In such a

inevitable.

but a constant

life

there

is

245

no peace,

between the insistence of
In one
desire and the powerlessness of will.
if
to
or
our
life
is
be
another,
great and
way
strife

we must escape

free,

this

prison and this

strife.

One way

of escape

is

by philosophic con-

templation. Philosophic contemplation does
not, in its widest survey, divide the universe



two hostile camps friends and foes,
helpful and hostile, good and bad it views
into

the



whole

impartially.

templation, when

it

is

Philosophic conunalloyed, does not

aim at proving that the rest of the universe
akin to man. All acquisition of knowledge
is an enlargement of the Self, but this enlargement is best attained when it is not directly
is

sought.

It is

obtained when the desire for

alone operative, by a study
knowledge
which does not wish in advance that its
is

objects should have this or that character,
but adapts the Self to the characters which
it

This enlargement of
when, taking the Self as

finds in its objects.

Self is not obtained
it is,

we try to show that the world

is

so similar

THE PROBLEMS OF PHILOSOPHY

246

to this Self that knowledge of

it is

possible

without any admission of what seems alien.
The desire to prove this is a form of self-assertion,

and like

all self-assertion, it is

to the growth of Self which
which the Self knows that it

an obstacle

it

desires,

is

capable.

and

of

Self-

assertion, in philosophic speculation as else-

where, views the world as a means to its own
ends thus it makes the world of less account
;

than

Self,

and the

Self sets

bounds to the

greatness of its goods. In contemplation,
on the contrary, we start from the not-Self,

and through

its

Self are enlarged

the

universe

greatness the boundaries of
through the infinity of the
;

mind which contemplates

achieves some share in infinity.
For this reason greatness of soul
fostered

those

is

it

not

which

asphilosophies
similate the universe to Man.
Knowledge is

by

a form of union of Self and not-Self
all

union,

therefore

it is

;

like

impaired by dominion, and

by any attempt

to force the uni-

verse into conformity with what we find in
ourselves.
There is a widespread philosophical tendency towards the view which tells

THE VALUE OF PHILOSOPHY
us that

man

that truth

is

is

the measure of

all

247

things,

man-made, that space and time

and the world
the mind, and

of universals are properties of
if

that,

there be anything not

created by the mind, it is unknowable and of
no account for us. This view, if our previous

but in

discussions were correct,

is

untrue

addition to being untrue,

it

has the effect of

;

robbing philosophic contemplation of
gives

it

value, since

it

all

that

fetters contemplation to

Self.
What it calls knowledge is not a union
with the not-Self, but a set of prejudices,

habits,

and

desires,

making an impenetrable

between us and the world beyond. The
man who finds pleasure in such a theory of
veil

knowledge is
the domestic

man who

never leaves

circle for fear his

word might

like the

not be law.

The true philosophic contemplation, on the
contrary, finds its satisfaction in every enlargement of the not-Self, in everything that

magnifies the objects contemplated, and
thereby the subject contemplating. Everything, in contemplation, that

is personal or
that
private, everything
depends upon habit.

THE PROBLEMS OF PHILOSOPHY

248

self-interest, or desire, distorts the object,

and

hence impairs the union which the intellect
By thus making a barrier between

seeks.

subject and object, such personal and private
things become a prison to the intellect. The
free intellect will see as

God might see, without

and now, without hopes and fears,
without the trammels of customary beliefs
and traditional prejudices, calmly, dispassionof knowately, in the sole and exclusive desire
a here

— knowledge

as impersonal, as purely
it is possible for man to
as
contemplative,
Hence also the free intellect will value
attain.

ledge

more the abstract and universal knowledge
into which the accidents of private history do

not enter, than the knowledge brought by the
senses, and dependent, as such knowledge
of

upon an exclusive and personal point
view and a body whose sense-organs distort

as

much

must

be,

as they reveal.

The mind which has become accustomed to
the freedom and impartiality of philosophic
contemplation will preserve something of the
same freedom and impartiality in the world of
action and emotion.

It will

view

its

purposes

THE VALUE OF PHILOSOPHY

249

and

desires as parts of the whole, with the
absence of insistence that results from seeing

them

as infinitesimal fragments in a world of

which

all

unaffected by any one
The impartiality which, in con-

the rest

man's deeds.

is

templation, is the unalloyed desire for truth, is
the very same quality of mind which, in action,
is

justice,

and

in emotion

is

that universal

love which can be given to all, and not only to
those who are judged useful or admirable.

Thus contemplation enlarges not only the objects of

our thoughts, but also the objects of our

actions

and our

affections

:

it

of the universe, not only of

war with

makes us citizens

one walled city at

In this citizenship of
the universe consists man's true freedom, and
his liberation from the thraldom of narr-^w
all

the

rest.

hopes and fears.
Thus, to sum up our discussion of the value
of philosophy
Philosophy is to be studied,
:

not for the sake of any definite answers to its
questions, since no definite answers can, as a
rule,

be known to be true, but rather for the

sake of the questions themselves ; because
these questions enlarge our conception of what

250
is

THE PROBLEMS OF PHILOSOPHY

possible, enrich our intellectual imagination,

and diminish the dogmatic assurance which
closes the mind against speculation but above
;

because, through the greatness of the
universe which philosophy contemplates, the

all

mind

rendered great, and becomes
capable of that union with the universe which
also

is

constitutes its highest good.

BIBLIOGRAPHICAL NOTE
The

student who wishes to acquire an elementary knowledge of philosophy will find it both easier and more
profitable to read some of the works of the great philosophers than to attempt to derive an all-round view
from hand-books. The following are specially recom-

mended
Plato Republic,
:

Transespecially Books VI and VTI.
by Davies and Vauqhan. Golden Treasury

:

lated
Series.

Meditations. Translated by Haldane and
Cambridge University Press, 1911.
Ethics.
Translated by Hale White and

Descartes

:

Ross.

Spinoza

:

Amelia Stirling.
The Monadology.
Leibniz
:

Translated by R. Latta.

Oxford, 1898.

Berkeley

Hume
Kant

:

:

Three Dialogues between Hylas and Philonous.
Enquiry concerning Human Understanding.
Prolegomena to every Future Metaphysic.
:

/

251

INDEX
places wliere a view is
discussed, not asserted.

The interrogations indicate
Absolute idea, 222
Acquaintance, 68, 69, 72
170, 211
vdth Self ? 78 ff.
Act, mental, 65
Analytic, 128
Appearance, 12, 24

ff.,

Correspondence of belief and
fact, 190 ff.
Critical Philosophy, 126
Deduction, 123

A priori, 116, 118, 125, 127ff.,

Descartes, 27, 114, 235
Description, 71, 74, 81
170

ff.,

136
Arithmetic, 130

Divisibility, infinite, 227-8
Doubt, 27, 28, 40, 234
Dreams, 30, 34-5, 172, 191

Association, 97, 101

Duration, 50

Being, 156
Belief, 186

Empiricists, 114, 134
Error, 172, 186 ff.,

1613.
mental ?

ff.

instinctive, 37, 39
Berkeley, 18, 22, 24, 56,
60 ff., 114, 149, 151
Bismarck, 85, 89

Bradley, 148

Facts, 214

Falsehood, 187

Coherence, 190-3, 218
12,

Contradiction, law of
129

ff.

definition of, 201

54-6,

13,

215
Contemplation, 244

Generalisation, empirical,
,

121, 125, 166

113,

Correspondence of sensedata and physical objects, 35, 38, 49, 52-3,

59, 62

:

:

Cogito, 28
11,

Excluded Middle, 113
Existence, 155
knowledge of, 93, 116
Experience
immediate, 9, 23, 27, 61
extended by descriptions,
92, 94, 231

Cat, 35, 36
Causality, 107, 129
Cause, physical, 35

Colours,

217,

236

Geometry, 120, 130
Hallucinations, 30, 172
Hegel, 221 ff.
Hume, 114, 129, 149, 151

253

INDEX

254
'

35
Ideas, 61 ff.,
abstract, 76, 149
innate, 114
Platonic, 142 ff.
Idealism, 58-71
defined, 58

43-6
Locke, 114
Logic, lUff., 144, 192, 231
Light,

Mathematics, 119, 130
Matter, 18, 68
existence

of, 60 ff.
56
Identity, law of, 113
Induction, 93-108, 123, 167
principle of, 103, 104, 175

grounds

Inference, logical and psychological, 209
Infinity, 227

of,

19, 20, 22,

26-41
nature of, 42-57
Memory, 76, 180-4
Microscope, 14
Mind, 19, 81
the only reality ? 21

Idealists,

what

ff.

is

in

62

the,

Monad, 148
Monadism, 148
Monism, 148

Judgment, 195-7

Motion, laws

Kant, 126-41, 229

Nature of a thing, 224

:

170
definition of, 204 fT.
derivative, 171, 207-9
intuitive,

8,

171,

Particular, 145
Perception, 177-9, 214

235
174-85,

210 ff, 232
of futme, 94 ff.
of

general
principles,
68
109-26, 131
of things and of truths,
69, 72, 170, 225
of universe, 40, 2''0, 241
only of mental things ?

64 ff.
theory of, "0
philosophical, 233, 239

99

Objectof apprehension, 65-'/
of judgment, 197

description, 70, 72-92,

?

of, 95,

Necessity, 121

Knowledge
by acquaintance and by

indubitable

i

I

I

Phenomena, 134
Philosophy, value of, 237-50
uncertainty of, 239-44
Physical objects, 18, 30 ff.,
53,81, 132, 170
Plato, 142 ff.
Principles, general, 109-26
Probable opinion, 217
Probability,96, 102,105, 114
Proper names, 84 ff., 145
Propositions, constituents
of, 90
Qualities, 149, 159

Laws, general, 104, 115
Leibniz, 22, 24, 50, 114, 148

ff.,

154

Innate, ideas and principles,
114
Introspection, 76

Rationalists, 114, 134

INDEX
Reality, 12, 17, 24
Relations, 139, 148, 151,
159, 224-6; multiple, 1947; sense of, 198
Resemblance, 150, 160
Russia, Emperor of, 70, 116
Self,

78

ff.

Self -consciousness, 77

Self-evidence, 176 ff.
degrees of, 183, 215

two kinds

of,

212

Sensation, 17, 132
Sense-data, 17, 23, 27, 36,
42, 73, 132, 213

certainty
Shapes, 15

of,

28-30

Solipsism, 33-8

45 ff., 227 ff.
Euclidean and non-Euclidean, 229

ijpace,

255

Space, physical, 47
Spinoza, 147-8
Subject, 197
Swift, 122

Thing

ff.

in itself, 134

Thought, laws of, 113, 136
Time, 50 ff., 135, 160, 227 ff.
Touch, 16
Truth, 186

ff.

definition
of,

201

Uniformity of Nature, 98
Universals, 76, 81, 142-57,
231

knowledge of,
213
not mental, 151
Verbs, 147

ff.

158-73,
ff.

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story of the

4.

A SHORT HISTORY OF WAR AND PEACE.
author of "Russia in Revolulion,"

94.

8.

51.

THE NAVY AND SEA POWER.

7.

present British supremacy thereon.
POLAR EXPLORATION. By Dr. W. S. Bruce, Leader of the
"Scotia" expedition. Emphasizes the results of the expeditions.

MASTER MARINERS.

By John

A

R. Spears, author of

"The His-

history of sea craft adventure

from

EXPLORATION OF THE ALPS. By Arnold Lnnn, M. A.
MODERN GEOGRAPHY. By Dr. Marion Newbigin, Shows the rethings

and

to

some of

the

THE OCEAN. A GENERAL ACCOUNT OF THE SCIENCE OF
THE SEA. By Sir John Murray, K. C. B., Naturalist H. M. S.
"Challenger,"

Ocean,"
84.

Perm,

A

lation of physical features to livinf;
chief institutions of civilization.

76.

G. H.

By David Hannay, author of
brief history of the
"Short History of the Royal Navy," etc.
navies, sea power, and ship growth of all nations, including the
rise and decline of America on the sea, and explaining the

tory of Our Navy," etc.
the earliest times.

86.

By

etc.

1872-1876, joint author of "The Depths of the

etc.

THE GROWTH OF EUROPE.

By

Granville Cole, Professor of

A

Geology, Royal College of Science, Ireland.
study of the
geology and physical geography in connection with the political
geography.

AMERICAN HISTORY.
47.

THE COLONIAL PERIOD

(1607-1766). By Charles McLean AnProfessor of American History, Yale.

drews,
82.

THE WARS BETWEEN ENGLAND AND AMERICA

(17S3-18I5).

Professor of American History, WilC. Smith,
liams College.
history of the period, with especial emphasis
on The Revolution and The War of 1812.

By Theodore

A

67.

FROM JEFFERSON TO LINCOLN (1815-1860). By William
Professor of History, Brown University.
The
MacDonald,
author makes the history of this period circulate about constitutional ideas and slavery sentiment.

25.

THE

39.

WAR

CIVIL
By Frederic L. Paxson,
(1854-1865.)
Professor of American History, University of Wisconsin.

RECONSTRUCTION AND UNION
Haworth.

A

(1865-1912). By Paul Leiand
History of the United States in our own times.

OTHER VOLUMES

IN

PREPARATION

HENRY HOLT AND COMPANY
34 West 33d

Sh-eet

New

York

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